{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "09a0732d",
   "metadata": {},
   "source": [
    "## 1.3 概率分布函数的图形\n",
    "\n",
    "常用分布函数在上表列出。\n",
    "\n",
    "此处以正态分布、F分布和卡方分布为例，使用python绘制各自的概率密度函数曲线\n",
    "\n",
    "#### 1.3.1 正态分布的图形"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dbaf9918",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as st"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "100a6fcc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 正态分布的概率密度函数图形，根据不同的均值和标准差绘制曲线\n",
    "\n",
    "# 设置字体为楷体\n",
    "plt.rcParams['font.sans-serif'] = ['KaiTi']\n",
    "# 用来正常显示负号\n",
    "plt.rcParams['axes.unicode_minus'] = False\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "# 模拟数据\n",
    "x = np.arange(-10., 10., 0.01)\n",
    "# 计算概率密度函数\n",
    "y = st.norm.pdf(x, 1.0, 0.5)\n",
    "# 标注文字\n",
    "# xy  显示箭头所标注的点\n",
    "# xytext  指定文本的坐标\n",
    "# weight  字体的粗细\n",
    "# color   字体的颜色\n",
    "# fontsize 字体的大小\n",
    "# arrowprops  指定箭头的相关属性（arrowstyle 箭头风格，connectionstyle连接风格，color 箭头和连线的颜色）\n",
    "plt.annotate('mu=1, sigma=0.5', xy=(1.0, st.norm.pdf(1.0, 1.0, 0.5)),\n",
    "            xytext=(0.3, st.norm.pdf(1.0, 1.0, 0.5) + 0.2),\n",
    "            weight='bold', color='steelblue', fontsize=14,\n",
    "            arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='steelblue'))\n",
    "\n",
    "y1 = st.norm.pdf(x, 0.0, 1.0)\n",
    "plt.annotate('mu=0, sigma=1', xy=(0.0, st.norm.pdf(0.0, 0.0, 1.0)),\n",
    "            xytext=(-3.8, st.norm.pdf(0.0, 0.0, 1.0) + 0.2),\n",
    "            weight='bold', color='darkorange', fontsize=14,\n",
    "            arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='darkorange'))\n",
    "\n",
    "# 扁平\n",
    "y2 = st.norm.pdf(x, 0.5, 2.0)\n",
    "plt.annotate('mu=0.5, sigma=2', xy=(3.0, st.norm.pdf(3.0, 0.5, 2.0)),\n",
    "            xytext=(3.0, st.norm.pdf(3.0, 0.5, 2.0) + 0.2),\n",
    "            weight='bold', color='g', fontsize=14,\n",
    "            arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='g'))\n",
    "\n",
    "# 更加扁平\n",
    "y3 = st.norm.pdf(x, -0.5, 3.0)\n",
    "plt.annotate('mu=-0.5, sigma=3', xy=(-2.25, st.norm.pdf(-2.25, -0.5, 3.0)),\n",
    "            xytext=(-6.0, st.norm.pdf(-6.0, -0.5, 3.0) + 0.2),\n",
    "            weight='bold', color='r', fontsize=14,\n",
    "            arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='r'))\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.plot(x, y1)\n",
    "plt.plot(x, y2)\n",
    "plt.plot(x, y3)\n",
    "\n",
    "plt.title('正态分布概率密度函数', size=14)\n",
    "plt.xlabel('随机变量', size=14)\n",
    "plt.ylabel('正态分布概率密度', size=14)\n",
    "# 限制y轴的最小值和最大值\n",
    "plt.ylim(-0.02, 1.1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31c0eec1",
   "metadata": {},
   "source": [
    "#### 1.3.2 X^2 卡方分布的图形\n",
    "\n",
    "卡方分布的概率密度函数在t分布中已经给出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9374195c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eoQghhLhJSIK3gbSAugCYzuywcyRCCCFuFpLgbUBXqE6Gdibr5DZ7hyKEEOImIQneBvy9PdirK6NjpAUvhBDCNiTB20CApwv/mirjHLcbTCZ7hyOEEOImIAneBgI8Xdilq+CUfRESjto7HCGEEDeBUpXglVIBSqmuSqlAe8diSQGeLuw0VTF+OL3VvsEIIYS4KdgswSulJiql1imlXsvnc39gDtACWKaUClJKOSmlTiillpu/6tsqXksK8HThgK5EtoMrnJEEL4QQwvqcbFGJUmog4Ki1bq2U+kEpVV1rffWi8AbAs1rr9eZk3wSIA6ZorV+0RZzW4ubsiKuLC2fdaxAhLXghhBA2YKsWfAdgmvn1IqDt1RdorVeYk3t7jFb8OqAV0EcptdHcA2CTBxJr8Pdw4ahLTYjZITvaCSGEsDpbJXhP4LT5dTwQcr2LlFIKGAIkANnAJqCL1roF4Az0uk6Zh5VSm5VSm+Pi4qwRu0VU8HJhr0NVyEmH8/vtHY4QQohyzlYJPgVwN7/2yq9ebXgM2An0A3ZqrWPMH28Gql+nzAStdTOtdbOgoCDLR24h/h4ubM+ViXZCCCFsw1YJfgtXuuUbAseuvkAp9aJS6l7zj35AIvCLUqqhUsoR6A+U2Z1iKni6sCs9EFx9ZKKdEEIIq7PVmPZMYJVSqiLQE+ihlHpJaz0uzzUTgGlKqRHAboyx+tPAb4AC/tZaL7FRvBbn7+lCfHoOVG0kLXghhBBWZ5MEr7VOVkp1ALoCH2qtzwLjrromwfx5XrsxZteXeQGeLqRl5ZIT2hinDV9BTiY4udo7LCGEEOWUzdbBa60TtNbTzMn9phPg6QJAckB9MGVD7G47RySEEKI8K1U72ZVn/h5Ggo/zMY6OlW56IYQQ1iQJ3kYqeBkJPpZA8AiEM3J0rBBCCOuRBG8jFcxd9OdTsyC8ibTghRBCWJUkeBsJ9DYm1J1PyYSKTYzNbjJT7ByVEEKI8koSvI14uzrh6uTA+RRzC16bjG1rhRBCCCuQBG8jSikCvVyJu2huwYOMwwshhLAaSfA2FOjtanTRewWBb4TsaCeEEMJqJMHbUJCXi9GCB6Ob/tRm+wYkhBCi3JIEb0NB3q7GGDxApeaQeBxSztk3KCGEEOWSJHgbCvRyJT41k1yTNhI8wKlN9g1KCCFEuSQJ3oYCvVwxaYhPzYKwhuDgLAleCCGEVUiCt6FArzxr4Z3dIbS+jMMLIYSwCknwNhSUd7MbgIgWcHoL5ObYMSohhBDlkSR4Gwo070d/OcFXag7ZaXBujx2jEkIIUR5Jgrehy9vVXswzkx7g1EY7RSSEEKK8kgRvQ96uTrg4ORB3qQXvFwmewTIOL4QQwuIkwduQUoogL1fOX9rsRimjFX9SWvBCCCEsSxK8jQV6u15pwQNENIf4w5AWb7+ghBBClDuS4G0syMvlym52kGccXrrphRBCWI4keBsL9HK9MoseoGJjUI4y0U4IIYRFSYK3sUAvVy6kmLerBXDxhJC6sqOdEEIIi5IEb2MhPsZ2tRdS847Dt4BTW8CUa7/AhBBClCuS4G0s2McNgHPJeRJ8peaQdRHi9tspKiGEEOWNJHgbCzEn+NjkjCtvyoY3QgghLEwSvI2F+Bi72Z3Nm+ADqoBHBVkPL4QQwmIkwdtYkJcrSkFs3i56pSCiFZxYZ7/AhBBClCuS4G3MydGBQC9XzuVtwQNUbg3xR+BirH0CE0IIUa5IgreDEB/X/3bRA0S2Nr6fXG/7gIQQQpQ7kuDtINTH7b9d9AChDcDJHU5IghdCCFFykuDtINjH7doueicXqNQMjq+1T1BCCCHKFUnwdhDi7caF1Cwyc67a2CayFZzdCZkX7ROYEEKIcqNUJXilVIBSqqtSKtDesVhTqK+xVC7u4lXd9JGtQZvk4BkhhBAlZrMEr5SaqJRap5R6LZ/P/YE5QAtgmVIqqDDlyqLgy5vdXJXgKzUH5SDj8EIIIUrMJgleKTUQcNRatwaqKKWqX+eyBsCzWuv3gYVAk0KWK3NCvK+zmx2Amw+E1IMTMg4vhBCiZGzVgu8ATDO/XgS0vfoCrfUKrfV6pVR7jFb8usKUU0o9rJTarJTaHBcXZ4XQLS/UN58ED0Y3/anNkJtt46iEEEKUJ7ZK8J7AafPreCDkehcppRQwBEgAsgtTTms9QWvdTGvdLCgoyNJxW4W/hzPOjuraLnowJtplpxmT7YQQQohislWCTwHcza+98qtXGx4DdgL9CluurFFKEeztln8LHmQcXgghRInYKmFu4Ur3ekPg2NUXKKVeVErda/7RD0gsTLmyKsTH9foJ3icM/KNkX3ohhBAl4mSjemYCq5RSFYGeQA+l1Eta63F5rpkATFNKjQB2Y4y5e19VrpWN4rW6UF839p/NZ717ZGs4uBi0Ng6iEUIIIYrIJi14rXUyxoS59UBHrfXxq5I7WusErXVXrXV7rfWj5u76q8sl2SJeWzC66K8zBg/GOHzaebhw2LZBCSGEKDdsNqZtTuDTtNZnbVGutAvxcSMlM4eUzJxrP4xsY3w/vsa2QQkhhCg3ysWktbKoop+xVO5sUvq1HwZWB89gOLbaxlEJIYQoLyTB20lFP2NxwOnE60y0Uwqi2hoJXmsbRyaEEKI8kARvJ5cS/JnE67TgwUjwF89A/BEbRiWEEKK8kARvJyHerjioGyT46PbG92OrbBeUEEKIckMSvJ04OToQ6uPG6fwSfIVq4BUi4/BCCCGKRRK8HYX5uRNzvTF4kHF4IYQQJSIJ3o4q+rlz5nqz6C+JagsXY2Q9vBBCiCKTBG9HFf3ciEnMwGTKp4UeJePwQgghikcSvB2F+7mTlWvifGo+O9pVqApeoTIOL4QQosgkwdtRRV9jqZyMwwshhLA0SfB2FGbezS7fpXJgJPiUs3DhkI2iEkIIUR5Igrej8Mu72d0owbczvss4vBBCiCKQBG9Hvu7OeLg4cia/LnowxuG9w2QcXgghRJFIgrcjpZSxVO5GLXgZhxdCCFEMkuDtrKKfOzE3WgsPRjd9SizE7bd8AEnH4P+U5e9rTTsnwDdh8D9n+KMLXDxt74iEEKLUkQRvZxV93a5/olxeVToY348st3Y4pd+p1bD6NejxEzx0HJQDLH/W3lEJIUSp42TvAG52Ff3cOZ+SSUZ2Lm7Ojte/yL8y+EfDkWXQ6hHbBmgPk1tAwoFr3+/0OZhyoOu3ENXdeK/+CFj1sm3jE0KIMkASvJ2F5zk2tkqQV/4XVu0IO6dBbjY4Opes0sNzYPnTkJEILV688n7sVlj6OFz4F8LbGq1kjyDjs/O7Yd5QSD4BdYbBiaXQ4BFo8gRM7QB174PMRNj6CXT4GKoPNModWwwrn4fk41Clr5GcnT1u/Fm/GWDKvjZu90BwuepvdGEP+FUr2d9DCCHKIemit7PICkayO5lQwDh8lQ6QlQKnNpeswtRYmDMEmj4Hd6+Hg38a72cmwZ89oHJnGL7L6PpeMupKucUjocZgGLwcdv8IHT+FOvdc+XznBDg6H7p8DeHmpX2JR2BmX2g4Cu7ZCvH7YM0bBX/mHQ6+Udd+XZ3cM5Nh+1fQ8Cbo1RBCiCKSBG9nEf5Ggj8Rn3bjC6PbA6rk4/DHFoB3BDQaBf7VoPVbxvtH5hjf27wNPpHQ/EU4OhdMucb757ZBjUEQ3BAC60FaHLj5X7lvVhIMmA3RPa+0+vdNgQp1jQTsVwWaPAVH/i74s8Ja9hQENYTqA4r95xBCiPJKuujtLNjbFRcnB04VlODd/aFiY2McvmMJxpxTYowEfolvtPH94inIiIcvA4yftQlyMiA9DjxDjW7wmHVGN3nCQahQ57/3bTgKHF2uqusUnN8FX/gZP5tyjK+CPrvRGHydYcbrvVPgyFy4d3sx/ghCCFH+WSzBK6VCtNaxlrrfzcLBQVHJ373gFjwY4/CrP4GMZHDzKV6FHsGQGnPl54snje/elSC4EfSdfuWzzERwMyf8CnXgnydh0UPQ+HGjJZ+X83XmD3hVguhe0PET42dtgqyLBX92ozF4MOYKLHkEbpsBXhUL93sLIcRNxpJd9I9b8F43lQh/D04mFCLBV+kAOrdku9pFdTNa4Lt+MMbB171tvncfSDkDZ9aBgxMcmglT2xut6sTDcHoV3LkaHjwI7T8qXF2174YzayFhvzGmv/NbmH17wZ/daAw+7RzM6A3NR0NoC2NeQlZK8f8eQghRThUpwSulQvJ5XwGDLRLRTSgywIMTFwqR4CNagpN7ycbhvStBr8mw4T34/RYIa2287+prjKFv+wx+qAl7fob+s41Z7b7R4B4M0zrA91XhUzeY2R9ys25cl2809PoVVoyGH2sbCb3fjII/u5F9UyD1LKx5HT73vvIlhBDiPwrsoldKRQEXgDDgLuDt61zWEpB/ZYspIsCd5IwcktKy8fW4wRI4J1eo3MYYhy+JGrcbX5fc+qHxPaQp3L3u2ut3/2hMnOs/y+iKTzxktKITDhgT7oYsz7+uqG4QtbPon+WnyVPGlxBCiBsqTAu+NdAPaA5UB1BKOSul3lJKXRoIHgl8bZ0Qy7/IgEtL5Qo5Dn/+ACTZcHvWyE7GPvg/N4BvQo1ldg0fNWbBCyGEKJVu2IJXSgUAW4AXgKNAFaXUFGA60ANorJTaCARpre+3drDlVSXzUrmT8WnUC/e98cVVOhrfjyyHxkOtG9glvtEwaLFt6hJCCGER+bbglVIOwEogA8jQWr9v/vkxwBEjyQ8E+gBLrB9q+XVps5tCzaQPrgOeQbIvvRBCiBu6URe9GzBQa30CuKCUqg+0A94HsgAfYDRwH1BDKeVp5VjLLR83Z3zdnQvXRe/gYMymP7IMTCarx1ZoMRvtHYEQQog88k3wWus0rfWl3UbigVzgM2CW1nomMAeYqrXeD3wOyHZiJRAZ4MGJ+AK2q72kWhdIjYOY7VaNqdBO/AMLhts7CiGEEHkUdplcMPAU0Biop5RqBGzSWh8F0FrvxXgAEMUUEeBe8G52l1TtbHw/VApGRrQ2TnNr9bq9IxFCCJFHYRP8RGAsMBU4AQwB/lZK/Z9SqpL5mjlWiO+mERHgwamEdEwmXfDFXkFQsQkcLAUT3w7NgtwMqHWnvSMRQgiRR6G2qtVaHzG/PAZsA6YBKKWqAC8ppbZrrb+/0T2UUhOBOsBcrfV71/ncF/gdYwJfKsZDhAk4Yv4CeEJrvaswMZc1Ef4eZOWaOJucQUXzEbI3VL0rrPwI0uLBI8D6AV6PKRfWvArtPzR2oxNCCFFqlOhfZa31Ea3148BupVTH/K5TSg0EHLXWrTGW2lW/zmVDgY+11t2AsxjL8BoAU7TWHcxf5TK5A0QHGnMUj51PLVyBal2N/dsP/2PFqAqwdzK4+ht7ygshhChVLNLs0lqvB5bf4JIOmFv9wCKg7XXu8ZXW+lKfcxBwDmgF9FFKbVRKTVRKXdPjoJR6WCm1WSm1OS4urgS/hX1FmRP80QuFTPDhTcA9wH7d9LlZsPZNaDcWlLJPDEIIIfJlsX5VrfWNBo89gUtbr8UD193THkAp1RrwNz80bAK6aK1bAM7ANU1FrfUErXUzrXWzoKCgYsdvb2E+brg6ORS+Be/gCFU7GRPt7LFcbucEqFAbKrWzfd1CCCEKVGCCV0oFKqXuzfNzcR4KUoBLA8te+dVr3jnvc+AB81s7tdaXzjbdjHmr3PLIwUERVcGTo4VN8GCMw6edt/1yuexU2PA+3PK+besVQghRaIVJ1t8ADwEopcYDTxajni1c6ZZviDFZ7z+UUi7AH8DLWuvj5rd/UUo1VEo5Av2BHcWou8yICvQoWoK313K5rZ9CpVshpLFt6xVCCFFohUnwycD35tZ1NvCZUupWAKXUCKXUo0qp/ua18fmZCQxTSn2McazsGqXUS1dd8yDQBHhVKbVcKTUEeAf4BdgOrNNal4KF39YTHejFifg0cguzVA7ss1wuPR62/A9uedd2dQohhCiywiT4nVrrSVrreOB14CXgf+bPKgI5QF8gMr8baK2TMSbarQc6aq2Pa63HXXXN11pr/zwz5qdqrXdrrRtoretrrV8t+q9XtkQHepCdqzmdUMgd7cDopj+1yVguZwubPoRqA8C/3I6WCCFEuVCYBJ+ulKqtlFoBBGutx2DuKtdav6O1ngBs11r/faObaK0TtNbTtNZnSx52+RRVoYgz6cFYLoe2zXK5lBjY9R20fsP6dQkhhCiRGyZ4pdTLQGUgDmPsfYJSqh2Qq5QKV0q9YF7jXtP6oZZ/0UFFXAsPeZbLLbJSVHmsfxfq3g/elQq+VgghhF3d6LjYEIx16HOBKOAZjCT/IOCBkfjPAxrwt3agN4MgL1c8XRyLNtHOwRGqdzMSfG6O9YJLPAz7p0GLq6dOCCGEKI1udJpcrNb6NoxtYmsBszB2mEsDfIGjWusftNYzgO1KqRq2CLg8U0oRFVjEpXIANXtCegKc3GCdwADWvAFNngSPQKtVcSzxGOrtsrlpTnZuNvW/rs/yY8vtHYoQQgCFG4M/B7ibE3lt4EVgGPC6eY38rxgz4+W0EQuIDvTkWFHG4AGqdQZHF9g/zzpBxe2EE0uh6TPWuX858OGaD9l9bre9wxBCiMsKc9hMN6C1UupvjONiu2NsRjMPqKq1vsd86IwsiraA6EBP5u8+S1aOCRenQu4p5OoNUe2MBN/tPctvHbv6VaNr3sXbsvctA1p814IDFw5c8/7nPT9nWMNhABy8cJDx68YT5Rdl4+iEECJ/hckgazA2qvkDYz/5TOAOrfUcoBJcPnTmT6tFeROJDvQk16Q5Udiz4S+p1Qvij8D5g5YN6PQaowXf8BHL3tdszoE5VPusGoEfBvLHv39cfn9rzFbaTGyD7zhfev/Wm7jUK+cM7D63m4bfNMT/A3+enP8kdb+qy+cbPgegw08d+Gn7T3yy/hOiPonir71/XS63+PBiGn7TEL9xfgybMYy07LQCP5sxZAbbH9l+zdeA2gMulx05ZyQv3fISlX0rW+VvJIQQxVFggtdaJ2utv9Ratze//j+t9Y/mjxdaOb6bTrVgLwAOnUspWsEaPY3vluym1xpWvwKt3wQnN8vd1yw2JZYh04fwXOvnWD9iPX/uNZ4RkzKS6PFrDzpHd2bXqF04KAdGzR11udzIOSMZXGcwy4cv58ftP/Jpj0+5p8E9lz+fsGUC8w/N5+veX9Mu0tgr/0jCEfpO6cuoZqPYOnIr+87v441lbxT4WbhPOFF+Udd8ebkY/51+3PYjSZlJPNfmOYv/fYQQoiRKelxsEbOQKEjVICNxHI4r4p/WNxzCGlo2wR9bCGnnoO69BV9bDAsOLSDCJ4JRzUdRLaAab3V4CzBa9QBvd3ybSN9IXrzlReYenEuuKReAbTHbGFR3EA1DG1IvuB5xqXH4u19ZyJGUmcTsu2bTs3pPgjyNA4im7JpC3eC6PNLsEar4V+Gplk/x9/6/C/zsRuJS43h56ctM7DcRJ4fCjHYJIYTtFPtfJaWUu9a6CFuuicLwdHUi3M+dg7EXi164Zi9YPg5S4oxtbEtCm4zW+y3vgpWSV0xKDJG+VzZAjPaLBuBU8ini0+MJ+CAAAJM2kZGTQVxaHKFeoVQLqMa6k+sI9Ajk4IWD1Amq85/7jmo2ChdHl/+8dyr5FLtid+E3zg+AHFMOOaacAj+70Rj8gsMLeLDxgzQKbVTiv4UQQlhasf7lVkpVBb4Eelg2HAFGN/3BonbRg7FcbvlYOLgQGt9T8PU3cmA6KAeofnvJ7nMDwZ7BxKTEXP75ZPJJACr5VKJRaCOmD55++bPEjEQC3I2EXyeoDk8ueJKHZj/E4y0ep2Fow//c91L3eV6VfCrRq3ovPunxCWA8NFzMvFjgZzOGzCDblH3N/QI9Arl35r14u3jz5aYvAUjJSqHPb324t+G9fNX7q+L8SYQQwmIK1UWvlHLL89oPYx28bG5jJdWCvTgcl4KpsIfOXBLaAHzCYf/8kgVgyoE1r0PbMZafkZ9Ht6rdOHjhID9s+4EjCUd4e8XbAPSp0YczF8+w7uQ6nBycmLlvJu1/bE+OKYfD8YdZdWIVq+9fzcEnDvJR148KVdfd9e9m7cm17D+/HwflwLebv+X2abcX+NmNxuCPPnWUnaN2Xp5416xiM77v9z3vdHzHOn8wIYQoggJb8EopH+AfpVRz4EPgFPADV853FxZWPdiLjGwTpxPTiQjwKHxBpYxW/PbfIDsdnIv5n2j3T+BVESp3LV75QqrkU4nJAyczevFoXv3nVYY1GMbqE6vxdfNl9l2zeXz+44yYPYKaFWoy+67ZeDh7EO0fTbBnMB0mdSApIwmlFL2r92baoGnXdMvnFe0fza8Df+X5Rc9zOOEwTcKaMGPIjAI/u5Grl8W5ObkR6hVKoBU3AxJCiMJSWuffSlRKVQKqAomACbhda/2W+bMdWuuG+Ra2g2bNmunNmzfbO4wS23wsnju+WccP9zWjU62QohU+tBR+HQh3TYWaxRhBycmAidWh7x9QsVXRy1vZxK0TmfrvVL7v9z1eLl4cij9E7996s2z4MuoF17N3eEIIYXNKqS1a62ZXv19QF70GOplfnwEmK6WmKqUUIBPsrKTYS+XA2PDG1Qf2zS5e5du/gpCmpTK5A3SK7oRG0+DrBoSOD2XI9CE82uxR6gbVtXdoQghRqhTURV8XCALaAX2AKcB+4AXAXyk1FLgIJGPsU39Aa22yXrg3Bz8PF4K8XTkYW4wE7+QCNXrAvrnQ5xNwdC582cxk2DgOBtvg6NliivaPZvGwxfYOQwghSr2CWvA9MXaua4ixNe0tQHXAE0gAKmLsZlcDaA5Us1qkN5lqQcWcSQ9Q5zbj8Jljq4tWbvP/QXQPCJSubiGEKOtumOC11s8AF4CfgaEYW9WGAjswdrH7W2v9ldZ6gtb6F631tQuGRbFUD/Hi8LkUbjRHIl/VOoOzJ+wteLOWy9LiYPsX0ObtotdXypikE0kIIQq1TG43sAmji/44MATYiNFVH2G90G5u1YK9uJiZQ2xyZtELO7tD9a6wdw6Yd38r0IYxUOsu8I0uen2lyJIjSxgwdUDBFwohRDlXmL3oZwKuwAwgAHgOiAEOI13yVnNpot3Bc8XY0Q6gTj9IPQcn1hd8bfIJ2PMztHqteHWVEiZt4sUlLzK0/lB7hyKEEHZX2L3oc4E+WusNGDPrPTAm1UkL3kqqBxtHsxZroh1A9W7GATGF6aZf9zY0GAmeocWrq5T4c49xWM0dde6wcyRCCGF/hUrwWusUrXWi+fVLWutkjJnzK6wY200t0MuFAE8X9p8tZgve1Ruqdoa9s8F0gzHpC/vg8N/QfHTx6iklckw5vL7sdcZ0GoODKtEZSkIIUS4U+19CrXWC1nqRJYMRVyilqBXqzd6zycW/SZ1+kHwaTm+58p7WkHr2ys9rX4emz4Fb2d55eNL2SYR6hdKtajd7hyKEEKVCiZo6SikfpdQtSqlHLRWQuKJ2mA/7z14kt6h70l9Sowc4OMPeWVfei98Hf/U2XsdugdNroMmTJQ/WjjJyMnh7xduM7TwWZcW984UQoiwpcoJXSl3a2Q5zV30a8LBSqlRtW1se1A7zITPHxNHzqcW7gbsfVOkAe/42Wu4A2XnuteoVY2KdcxH2uy+Fvt70NY1CG9E6orW9QxFCiFKjwASvlApTSr1vfu0A/Ke1rrXeBiwH8j/pQxRLrVBjot2+knbTJx6HmO3Gz6ZscHSBE8sg8SDUHwGxW+Hfn0sesB0kZyYzbs043u/0vr1DEUKIUqUwy+RigK5KqUnAY4BSSgUqpTorpSorpaKAesA+64Z686ke4oWjg2JvTAkSfK0+Rjf9LvPZ6rlZ4OACq1+G1m/B1k/hzx7g6muRmG3t43Uf07VKV+qH1Ld3KEIIUaoUeFys2RxgGeANNMbYxe4i8D2QCtyntS7mdG+RH1cnR6oGebIvpgR/Wo8AY2e7f2dA13eNFnxmIuRmwr+TjO9DN4JvlKXCtpm41Dg+3/g5mx7aZO9QhBCi1CnsGPxRjJ3rugJhwHjgJWAwcEJrfco64YnaYT7sK+5SuUvq3WHMpj+xDnLSIX4vpMVCpfYwZHmZTO4AY1eP5c66d1LFv4q9QxFCiFKnMGPwjsD7wDcYG9x8AywAugFPASOVUrLhjZXUCvXhdGI6SWnZxb9JzZ7g5A67/4TUWHBwggFzoM2bxusy6GTSSSbtmMRr7cv27ntCCGEthRmDz8U4JnY0MBPwBWoDjkAcMAq4y3oh3txqh1lgop2rl5Hk98yEusPhyVQIv8UyAdrJ2yve5uEmDxPmHWbvUIQQolQqbBf9CYwu+U4Y+8+3AIKBzUBNYLqSBchWUTvMB6BkE+0A6t8BaRfgyAoo4/+p9p/fz6z9s3jhlhfsHYoQQpRaN0zw5u55tNZfYrTW38GYYJeptR4F9ANOaa2P6ALONVVKTVRKrVNKXbdPVSnlq5Sar5RapJSaoZRyKUy58i7Y25UAT5eSj8NX6wJuvrB7umUCs6PXl73Os62exd+9bO++J4QQ1lRQC36xObn+DLQGVgO/AS2VUj8BYzBa71OVUrfndxOl1EDAUWvdGqiilKp+ncuGAh9rrbthHGTTo5DlyrVLW9buKWkL3skVavc1jpDNTrdMcHaw5cwWVp9YzZMty8Due8eOld3ekiFD4Ikn7B2FEKIECpphNURrHQeglHID3sA4C/42YLzW+l+llDMQidGNn58OwDTz60VAW+Bg3gu01l/l+TEIOAfcXVC5m0H9cF9+XHOMrBwTLk4l2F243h2w7Vc4uAjq3Ga5AG3olX9e4bX2r+Hp4mnvUMqvefNg2TI4cMDekQghSuCG2eJScje/zgBWmM+HHwF0V0o111pna60Pa61vNM3bEzhtfh0PhOR3oVKqNeCvtV5fmHJKqYeVUpuVUpvj4uKu/rhcqBfuS1auiQOxJeymj24PnsFXNr0pY5YfW87BCwcZ0WSEvUMpu1q0AD+/a79++cX4PDUVHn0Uxo0z3hdClFlFag5qrReav+dqrT8GzheyaArgbn7tlV+9SqkA4HPggcKW01pP0Fo301o3CwoKKmQ4ZUuDSsYuc7tOJ5XsRg6OUG8gHFgI6YklD8yGtNa8vPRl3un4Di6OpXhX5DlzoFo1CAyEP/648v7WrdCmDfj6Qu/ekPdhdPduaNgQ/P3hySehbl34/HPjsw4d4Kef4JNPICoK/vrrSrnFi41yfn4wbBikpRX82YwZsH37tV8DBhifv/02ZGWBkxMsWnTjo4aFEKVaiU6T01ofLeSlWzC61wEaAseuvsA8qe4P4GWt9fHClrsZRAZ44OPmxM5TJUzwAA2GmHexm1Hye9nQ7AOzSclK4a56pXhFZmysMXb93HOwfj38+afxflIS9OgBnTvDrl3g4ACjRl0pN3IkDB4My5fDjz/Cp5/CPfdc+XzCBJg/H77+Gtq1M947cgT69jXus3Ur7NsHb7xR8Gfh4caDwtVfXl5w/LhRd3S0cY+XXjLuI0leiLJJa33DLyAc6FTQdQXcwwfYAXwM7AUqAy9ddc0oIAHj4JrlwJDrlPO9UT1NmzbV5dXd363TfT5bVfIbmUxaf9FC6++7lvxeNpKTm6PrfVVPz9o3y96h3NhPP2lds+aVn+fP1xq0/vVXrYOCtM7NNd5ftUprNzetc3KMn93dtd6/33jdqpXWv/125R633qp1nTpaZ2b+t6733tO6SZMrP//yi9bVqxf82Y28/bbWERFap6cbPycna+3vr/XcuQWXFULYDbBZXycnFmYbsx4Ym9r8A6CUGoIxoe601vpGE+vyPkQkK6U6YGx1+6HW+iww7qprvga+vrrsVeUs0IQtm+qH+zFx9REyc3JxdXIs/o2UgoZ3wZI34cJhqFDVckFayZTdU/By8aJvjb72DuXGYmIgMvLKz9HRxvdTpyA+HgICjJ9NJsjIMLrpQ0ONLv1164xu/YMHoU6d/9531ChwuWpY4tQpozfg0jh5To7xVdBnLVpcf/Lc558b5Tp2BDc34z1vb6heHY4WtqNOCFGaFCbBJ2HMakcpFY2xNG4NEGZettZNa13gdFutdQJXZsQXWnHLlTcNKvmSnas5cDaF+pVKePJbgyGw9G3YMQU6le7tBbJys3hj2Rv8eNuPlPq9lIKDjSR/ycmTxvdKlaBRI5ieZ3JjYuKVhF+njjH2/tBD8Pjjxth5Xl5e19ZVqRL06mWMzYPx0HDxYsGfzZgB2deZDxsYaCTyXbuuvGcyGUn/0oOKEKJMKcwY/GGMrnIw1qd/o7W+F7gDmFaY5C5Krn64kdR3nk4s+c18wqBKR9jxe6kfX/1uy3fUqFCDW6NutXcoBevWzWiB//CDMYb99tvG+336wJkzRivdyQlmzoT27Y1W9eHDsGoVrF5tlP3oo8LVdffdsHYt7N9vjOl/+y3cfnvBn91oDH7QIJg713gQOXUKXn4ZMjOvjPsLIcqUwiT4E0AFpdRjGOPijZRSg4BewEal1G1KqQ5KqdqXdr4TllfJ3x0/D2d2WWKiHRjd9Ekn4fgay9zPClKzUnl/1fuM6TzG3qEUTqVKMHkyvPce3HILtG5tvO/rC7Nnw2efQc2a8PPPxs8eHkbrODjYmC1ftarRPd6/vzGT/Uaio+HXX2H0aKhd20joM2YU/NmN1K4Nv/8O775rdM3PnQuzZhld9UKIMkfpfHaYNe8t/w7wF/AMcAajNd8N43x4AA2YzF8ZwAat9elr72YbzZo105s3b7ZX9VY3bOIG4lOzmPukBVpUWWkwvgbU6Qf9vyr4ejsYu2os285uY9qgcjxCM3EiTJ0K339vtKIPHTKW0S1bBvXq2Ts6IUQZoJTaorVudvX7NxqDD8SYXPcRUAV4UGu9TCnlp7WeZKU4xQ3UD/dlwsojZGTn4uZcws4SFw+o299YLtfrIyhlO8MlpCfw8fqPWX3/anuHYl2dOhmt5gYNjLXq4eHGRjN169o7MiFEGZdvgtfGLnavACil/gDuUkrdA1RWSjUA3IALwP9prW+67WPtoUElP3JMmn/PJNO0sgUOWml0N2z7BfbOhoZ3lvx+FvThmg+5reZt1Aysae9QrCs62tiURgghLKywG92kYaxT/wmjO/4drfUg4E1J7rbTpLIfANtOJFjmhpGtwT/K2J++FIm5GMOErRN489Y37R2KEEKUWYVZJgfGBjRVtdarlFJ3AROUUk9rrU9aMTZxlWBvNyr5u7O1BAn+fPp5dp/fzdGko5xJOUNqpSjSY3fjuuRxPD1DCPYIprJPZar6VaWqX1UcVIk2OyyW91a+x30N7yPCN8LmdZdKmZng6mrvKIQQZUxhE3wsRnc8WusL5q76d4DR1gpMXF+TSH82Ho0vUpnjyceZdWgWy04u41Diocvve7t44+PkgZuzM5lnN5Pq5EJC5pWHBx8XHxoHN6ZteFs6R3YmyMP6e/0fjj/M7//+zv7H91u9rjLh+HFjmdqJQu0pJYQQlxUqwWutx171c7pS6iOlVEOt9Q7rhCaup0mkH3/vOMOZxHQq+rnf8Npt57bxzY5vWHtmLQ7KgeahzelbtS9NgptQxa8KPi7m7Q2m3A2nNsGze0jXOZxIPsH+hP1sjd3KprObWHFqBWM2jKFJSBPuqHEH3Sp3s9qBL28uf5MnWzxJoEegVe5f5rz1Fgwfbu8ohBBlUGFb8NfQWp/DOLNd2FAT8+S6rScS8k3wpy6eYuzGsaw8tZIAtwCebPwkt1W7jWCP4OvftOlw2D8X9s/HvU4/agbUpGZATfpV7QfAoYRDLD6+mDlH5vDyqpf5cOOH3F7jdu6pfQ8V3CtY7HfbFbuLxUcW83Xva3Ysvjnt2WOsRT8o01yEEEVX5ASvlAo17yUv7KB2mA9uzg5sPZ5InwYV//OZ1ppf9/7KZ1s/QynFM02f4a5ad+HudOOWPtW6gE84bPnJWBd/9cf+1ajmX42RDUeyPmY9U/dN5YfdPzB572QG1xjMffXuI9C95C3uV/95lZfbvoy3q2ysAsDrr8MLLxgb5QghRBEVZwbVJ5YOQhSes6MDDcL9rplol5yVzFPLnuLDTR/SMqwlf/f/mwfqPVBwcgfjnPjGw+DwP5BwPP/LlANtKrbh006fMvO2mXSO7Mwve3+h11+9mLBzAhk5GUX6XZYeWcq7K94FYO3JteyI3cEjzR4p0j3KrY0bYcMGeOwxe0cihCijipTglVLNMXayE3bUuLIf/55JIiM7F4AzKWcYOncoq06t4oXmL/B5p88J9Qwt4k3N548XcslctG80Y9uNZdZts7il4i18vu1z+s3sx4KjC8hvd8SrHUs8xtHEo2iteWXpK7x565u4ObkVLe7y6pVXjDPc3QvxgCaEENdR6ASvlPIHfgXWWy8cURhNIv3JztXsPp3EgYQD3DPvHi5kXOC7bt8xrM6w4p265hdhdNVv+xVycwpdLMo3iv91/B8/dP8BHxcfRq8czagloziTcqbAslm5Wbg4urDo8CJiU2O5t+G9nE87z5mLBZct15YuNWbP33+/vSMRQpRhhUrwSikfYBGwHHhaKbVQKdVJKSVTne2gSaQx0W7xwZ08uPBBFIpJPSbRLPSarYiLpul9cPEMHCr6zmrNQ5sztc9UXmrxElvPbaX/rP78uudXck25+ZbJNmXj5ODEK/+8wrsd32XR4UXU/7o+y48tL/7vUNZpbbTe330XnJ3tHY0QogwrMMHnabm/rbUeCQwEXIF7gWlKqaNKqS/MDwHCBoK8XakcnM4fp1/DycGJH3v8SHX/6iW/cY3u4BUKmyYWq7ijgyNDaw9l1m2zaBrSlA82fcD9C+/ndMr1zx/Kys3ieOJxtNasOL6CR+Y8wu+3/87d9e8uyW9Rts2caZwkN3iwvSMRQpRxN0zwSql6wDhgpNb60glym4B3tdb3aa07AfUAT2ChVSMVlyVlJpEZ+C3Zpmy+6fwtkT6RlrmxozM0e8BowV84XOzbhHmF8VXnrxjTdgwHEg5wx993MO/IvGuuy8zJZNmxZSRmJBKbEsuOR3aUjXPfrSU3F157DcaMMc5xF0KIEijoX5GRwKNa65g8760Gaiml3AC01qnAIYyz4eU8eCvLMeUwesVoMjhP2sl7yc4IsWwFTe8DB+dit+IvUUrRt2pfpvedTjW/ary46kVeXvUyKVkpl6/ZEbuDjJwMXmv/GlPvmIq/uwUO0CnLfv0VKlSAHj3sHYkQohwoKMG/Czgopb5SSgUAaK0zgfuBo0qph83XfaS1fkprnf+Aq7CIT7Z8wrqYdTzZ8EVy06OKvG1tgbxDoM5txmS7zJSCry9AJe9K/NjjRx5t+Cjzjs5jyJwh7I83tqF9vf3rrHtwHQ80fqB4EwPLk8xMePNNGDsWbva/hRDCIm6Y4M271UUCUcA6pVQb80ebgPpAuFLqL0BmA9nAylMrmbRnEkNqDuGBhncSEeDOhqMXLF9Ri4chMwl2TbPI7ZwcnBjVaBQ/dv+R9Jx07pl3D7MPz6Z+SH2ahze3SB1l3rffQr16cMst9o5ECFFOFDjQp7U+rLXuBXQGXlJKdQdOaK3Pa63fxDh05gsrx3nTO59+ntfXvE51/+qMbm6c8dMiqgIbj8ZjMhVu3XmhRbSA0Aaw8TtjVreFNAlpwrS+06gXWI9XVr/Ce+vfIys3y2L3L7NSUoxx9/fft3ckQohypNAzebTWp4DbgK7AjDzvbwc+Vkp1tXh0AjC2oH1z7ZukZKXwQbsPcHU0jg5tWSWAhLRsDsWVvCv9P5QyWvHn9sDxNRa9daB7IN91+477697P1P1TuX/B/cSlxVm0jjLnk0+gUydo2NDekQghypEiTdXVhueBW696fxewypKBiSsWHFvAylMrearJU/9ZDtcq2jjoZcMRK3TT178D3P1h4wSL39rJwYlnmz3Lxx0+5mDiQe6ceyd7LuyxeD1lwoULRoJ/5x17RyKEKGeKuxbnmn/1tdZF24hcFEpSZhLjNo6jboW6DK099D+fRQS4E+brxnpLT7QDcHY39qffOweSTln+/kDXyl35pecvOCgHhs8fzuLjRd9gp8z74AMYNAiqVbN3JEKIcqYoW9Ve3iRcF3azcVFi/9vyP5Iyk3irzVs4Ovx3FaJSilZVKrDu8AXLj8MDNB8BaKu04i+pGVCTKb2nUCOgBs8uf5Zvd3xb6L3sy7zTp2HiROPUOCGEsLDCblV7B9DLyrGIq+y5sIe/Dv7FPbXvoVZArete07ZaIPGpWeyJSbZ8AP6VjSVzm3+CzIuWv79ZoHsgP3T/gd5VevPF9i94adVLN8fku3fegREjoGLFgq8VQogiKmwLPhCoYM1AxH9prRm/eTx+rn6MbDgy3+vaVjeOA1h96Lx1Amn9hLFkbusv1rm/maujK2PbjuWJxk8w7+g8Ri4eSXKWFR5aSouDB+Gvv+DFF+0diRCinCpsgt8H+AIopXorpd5XSl2/SSksYtnJZWw6u4lHGz2Kt4t3vteF+LhRI8SL1QetlOArNYXI1rD+6yKdMlccSikebvAwY9uNZXvcdobPH87Z1LNWrdNu3ngDnn4aAgLsHYkQopwqbIL/F6MVD/Ak4AV8qZTaq5R6QSnlapXoblI5phz+t+V/VPGtwh017ijw+rbVgth4LP7y+fAW1/pxSDoBe/+2zv2v0qdKH77u8jVnU88ydO7QyzvflRvbt8Py5fDUU/aORAhRjhV02EyQUmqk1joOuNSMXGjelrYz0A4IA7YrpfysG+rNY/7R+RxLPsaTjZ/EycGpwOvbVQ8kK8fEpmNWmE0PULMnBFSFtZ9bdOObG2kV1oqfevwECu5bcB/rY9bbpF6bePVV40hYLy97RyKEKMcKasG/DFQ2v/ZXSv0BXD4WVmt9HvjKfB+ZKWQBOaYcJuycQE3/mnSK7FSoMi2rBODsqKzXTe/gCK0fhTNb4cQ669RxHTUDajK512RCPUMZtWQUc47MKbhQabd6NezZAw8/XPC1QghRAgUl+IXAa+bXKcB0oK5SaqpSKtr8fgjQSGt9k+5UYlmXWu+jGo4q9AEsHi5ONIn0Z5W1EjxAw7vBPQDW2nZX4lDPUCb1nETj4Ma8vOplfv73Z5vWb1Faw8svw9tvg6uMagkhrKugw2YWaq1N5h9jgDla60HAe8AkpdRArfVqrXV6QRUppSYqpdYppV67wTUhSqlVeX52UkqdUEotN3/VL9yvVTblmnIvt947RnYsUtl21QPZE5PM+ZRM6wTn4mGsi98/D+JsOybu4+LDN12+oUtkFz7a/BGfbf2sbK6Vnz8fEhJg6NCCrxVCiBIqyk52B4G6cHlr2u7AHUqpfgUVVEoNBBy11q2BKkqp6te5xh+YBHjmebsBMEVr3cH8tasI8ZY5S04s4VjyMUY2HImDKtomg22rBwFYr5seoOUjxg53qz62Xh35cHF0Yfyt4xlYfSDf7fqO9ze8T66pDJ1ObDIZ4+7vvQeOjgVfL4QQJVTUBN/k0g9a63St9d1AJ6VURAFlOwCXzh5dBLS9zjW5wBAg7+LnVkAfpdRGcw9AwTPOyrCf9/xMhHcEnSIKN/aeV/1wXyp4uvDPvnNWiMzMswI0vR92/QHxR61XTz4cHRx5q/Vb3F/POKjmpVUvkZ2bbfM4imXqVHBzg9tus3ckQoibRFESfGw+1z8P9CigrCdw2vw6HmPc/j+01sla66Sr3t4EdNFat8A4c/6a3fSUUg8rpTYrpTbHxZXdU8l2xO1gZ9xO7ql9zzVb0haGo4OiQ81glu8/R06uqeACxdXmCWPS3ZpPrVfHDSileLbpszzT9BkWHFvAE8ueIC07zS6xFFp2trEd7Zgxxkl9QghhA0VJ8GcwutD/Q2udA/xeQNkUwN382qsI9e7UWseYX28Gruna11pP0Fo301o3CwoKKuRtS59f9vyCt4s3/av1L/Y9utQOJjkjhy3HEywX2NV8wqDRUNg+GZLPWK+eAjxQ7wHeav0W686sY+TikSRlXv1sWIr88ANERxtHwgohhI0U5Tz4LK11aj6fFbRR+RaudMs3BI4VstpflFINlVKOQH9gRyHLlSlnUs6w+Phi7qh+Bx7OHsW+T9vqgTg7Kut20wO0fRpMuTafUX+122vczvhbx/PvhX+5b8F9pfNc+fR0ePddo/UuhBA2VJTT5HoppRoUs56ZwDCl1MfAYGCNUuqlQpR7B/gF2A6s01ovKWb9pdrv+39Hobir1l0luo+3mzMtoyuw1NoJ3j8KGgyGLT9CqhXOoi+CrpW78mXnLzmdcpph84dx8uJJu8ZzjS++gJYtoXlze0cihLjJFKWL/hYgsjiVaK2TMSbarQc6aq2Pa63H5XNthzyvd2utG2it62utXy1O3aVddm42sw7N4tZKtxLmFVbi+3WqFcyhcykcv3DdzhbLafssZKfD+i+tW08htK7YmondJpKSncLw+cM5lHDI3iEZkpLgo4+MmfNCCGFjBSZ4pZSz+WUs4J/n/aFKqUJPCdZaJ2itp2mty+npIcWz7OQy4jPiub3G7Ra5X+fawQAs3WvlVnxQDeMo2Q0TIM1KW+QWQf2g+vzY/UcA7lt4H7viSsGKyvHjoU8fqF3b3pEIIW5ChWnBf23+vgcIBlBKtQI+wJj4Jkrgz4N/EuoZyi0Vb7HI/SpX8KRasJf1x+EBOrwEWSl2m1F/ter+1ZnUcxJezl6MWDSCjTEbbRtATAz07Gm8jo2Fr76Ct96ybQxCCGFWmAR/USkVDuzEOFgGoC/QS2t9Ov9ioiCnU06z7sw6BlQbUKylcfnpXCuYDUcvkJRu5TXiwbWh/h2wcQKk2OCBohAivCP4uefPVPSqyKglo1h2YpntKr9wAU6a5wC8/z4MGwaRxRrVEkKIEivoNLnhgBvGDPZmQJRS6k6MsfRKSqm+5q8OSik5bKaI/jr4FwADqg2w6H271wslO1ezdG+sRe97Xbe+BDkZsPoT69dVSMEewfzY/Udq+NfgmeXPMPvwbNtUnJUFLi5w7BhMnmzsXJecDNu22aZ+IYTII98Er5QKxtjE5tKi6jCgKtDe/DoI44z45sBI4FGrRlrOmLSJWYdmcUv4LRaZXJdXo0p+hPm6MX+3DaY7BFaDhnfBpu/tui7+an5ufnzf/XuahjTlldWvMGXfFOtXmp0Nzs5Gt/xjj8HRo9C4McyYYf26hRDiKvlu/aq1Pgf853AXpVQT4BmtdZa1AyvvtsRuITYtlueaPWfxezs4KHrUC2XyhhOkZObg5WrlHX5vfQF2ToVV/we9/8+6dRWBp7MnX3X5iueXP8eHa94nLTme+xuOQLm4FPqkviLJyoKcHJg7F0aOhH794JtvYIBle2iEEKIwivov/zGgEWDj2Uvlz9wjc3F3cqdDRAer3L9nvTB+XHOMf/ado19DK4+e+EdB43tgyyS45Snws924s87KIuv4cTIPHyHzyGGyj58g5/x5cuLiyDl/HlNaGo9mZvKo1sAX7MfYnEc5O+Pg6YljQABOAQE4BgTgHBaGc+VIXCIr41I5EueKFVFFORgmKwsOHYIKFWDtWtiyBSpVss4vLoQQBShqgj+C0SUvCb4EsnKzWHR8EZ0jO+Pu5F5wgWJoWtmfIG9XFuyOsX6CB2g/Grb/BsvHQf+vrFZNblISqRs2kL5tO+nbt5Oxezc6+8pkQqfQUJyCg3GuVAn3hg1x8PbGwc0VXFxYdmYlu8/uoL5fbdoFt0KnppIbn0DuhQtkHjpEysqV6IyMy/dS7u641ayJW506uNWpjVuDBrhWq4ZyyGdk68QJY8x99Gjj3Hc5NU4IYUdFTfAxGGPwogRWnV7FxayL9K7S22p1ODooetQNZfqWU6Rl5eDhYuVuet9K0OJhWPcltH4MQupa7NZZx45xcek/pCxfTtrWrZCbi3Jxwa1ePfyHDcOtdm1cq1bBJToaB/f8H5gG6ZHEbv+Cd3ZOoFvlyoxrNw5nR+fLn2utyTkXR/aJ42QdP07GgQNk7NlD0syZJPz2GwCOfn54NG+GR7NmeLRsiWvNmle6+wcPhlq1oHVri/3uQghRXMVJ8H9ZI5Cbybwj8whwC6BVWCur1tOzfii/rD/Oiv1x9Kxv2Yl819XuOdj2Cyx+E+6ZXqJb5SYmkjRvHkmzZpGxYycArjVrUmHECLxubY9bvXo4uLgU6Z5KKZ5o/AQ+Lj6M3zye1JxU/tfhf5d7UZRSOIcE4xwSjEeerWW1yUTW8eOkb91G2ubNpG3axMXFxq7JTiEheLVvj1eHW/Fs3RoHSe5CiFKiSAlea30UsP1B4OVISlYKK06tYGD1gTg5WLdV3SIqgAqeLszZGWObBO8RYCT5xW/AkeVQpUORb5Gxfz/xP/9M8uw56KwsXGvUIPiFF/Dp0R3nipYZahhedzjeLt68ve5tRi4eyRedv8DHxSff65WDA67R0bhGR+N3+0AAsmNiSF27jpQVK0ieN4/EP/5Aubjg2bo1Pr164tW5M45eXhaJVwghisPK/bbiaitOrSAzN5Oe0T2tXpeTowN9GoTx+6aTXMzIxtvNueBCJdViJGz8zkjyDy2H/Marr5K6fgPnv/mGtPXrUe7u+A4cgP+QIbhZaZvXgdUH4unsyUurXuLBhQ/yTZdvqOBeodDlncPC8Lt9IH63D0RnZZG2dSspy5aRvGgxKStWGMm+fTt8evbEu1OnGw4dCCGENSittb1jsJhmzZrpzZtL9+65zy5/lm3ntrF00FIcVFHO+imerScSGPjVWj66owGDmkVYvT4AdkyFGQ/DwO+hwaAbXpq2ZQtxn31O2oYNOAUHE3DvMPzuuANHPz+bhLr69GqeWfYMoZ6hTOg6ocR7EmiTifTtO0ieP5+LCxaQExeHg6cnPr1743fH7bjVr2+dJXpCiJuWUmqL1rrZNe9LgredjJwM2k9tT98qfXm99es2qVNrTYfxy6nk787kEdYd87/MZIIJ7SE9CR7fBM5u11ySdeIEseM+IOWff3AMDCTw4YfxGzIYB1dX28SYx9bYrTy+9HE8XTz5rut3RPlGWeS+OjeXtM1bSPrrL5IXLkRnZOBavTq+tw/E97bbcPL3L/gmQghRgPwSvPWbkOKydWfWkZ6TTufKnW1Wp1KK/o3CWXv4AmeTMgouYAkODtD1XUg6ARu+/s9HptRUzn38P4707kPa+vUEPfss1RYvIuDeYXZJ7gBNQprwQ48fyMrNYviC4eyL32eR+ypHRzxbtqDiB+OovnoVoW+/jXJ359y4DzjU/lbOvPgi6btKwal3QohySRK8DS09sRRvF2+ahzYv+GIL6t84HK3h7x02PBuoakeo0RNWjofkGABS163jSN9+XJgwAZ9ePakyfz6BDz9UKsanawXU4qceP+Hi6MIDCx5g2znL7h/v6OWF/5DBRE+bSvTfs/AbNIiLi5dwbNBgjg25kyTzpEIhhLAUSfA2kmPKYfmp5XSo1AFnBxtMdssjOtCThhF+zNhm473iu78PuVnkznmNmDff4sT9D6BcXKg8+VcqfvABziHBto2nANG+0fzc42cquFfg4UUPs+b0GqvU41ajBqFvvE61lSsIeeUVchMTOTN6NAc7dybuyy/JSUgo+CZCCFEASfA2siV2C0mZSXSOtF33fF4DGlVkb0wy+84m267SClVJCxnCkfErSZw2jYAHHiB65gw8mja1XQxFFOYVxk89fiLKN4rH/3mcRccWWa0uRy8vAu4dRpX584j4bgJutWtz/vMvONSpM2ffH0P2aTmNWQhRfJLgbWTZyWW4OrrSJryNXerv1ygcZ0fF1E0nbVKfNpm48P33HP90OcrRkcpD/Ah5/jkc3K6dcFfaVHCvwMTuE6kfWJ/RK0dfPtbXWpSDA17t2hE5YQJVZv+NT7duJEyZwqFu3Tnz4otkHDhg1fqFEOWTJHgbWXVqFS1CW1ht7/mCBHi60K1uKDO2nSYjO9eqdeUkJHBq1KOcG/9/eHfpQvRnL+PBv7B9slXrtSQfFx++7fotrSu25s21bzLp30k2qde1enUqfjCOaosWEnDPUJIXL+Fov9s4OfIR0rbKufJCiMKTBG8Dx5OPc+LiCdpVamfXOO5sHkFiWjaL9sRarY7Mgwc5NmgwqWvXEvL6a4R/8j8cW90LlVrAkrcgPdFqdVuau5M7n3f8nG6VuzF+83g+3/Y5tlpW6lyxIiEvv0z1f5YS+OQTpO/cyfG77+bEAw9KohdCFIokeBtYdWoVAG3D29o1jluqBlLJ352pm05Y5f4pK1Zw7M67MGVmUHnyrwQMHWps6qIU9B4P6fGw9G2r1G0tzo7OfNj+QwZWH8iEnRMYu3EsJm2yWf2Ofn4EPfoo1ZYuIfiFF8jYv18SvRCiUCTB28Dq06uJ9o0mwttGO8nlw8FBMaRZBGsOXeDEhTSL3VdrTfykSZwc9SjOlSOJ/uMP3Bs0+O9FYQ2h5SjY/AOcLFunDTs6OPJW67e4r+59TNk3hVdXv0qOKcemMTh4eFDhgfuptniRJHohRKFIgreytOw0Np3dRLtw+3bPX3JHs0o4KJi62TKteK015z78iNix4/Du3ImoX3/FOTT0+hd3fAV8KsHspyA3+/rXlFJKKZ5t+ixPNn6SOUfm8OzyZ8nMzbR5HDdK9Ok7d9o8HiFE6SUJ3so2nd1ElinL7t3zl4T5utOxZjBTN50iK6dkXc06J4eYV14l/scf8R86lPBPP8XBwyP/Aq5e0OsjOLcH1n1RorrtQSnFQw0e4pWWr7Ds5DIeW/IYqdmpdonlmkS/dy/HBg/h1BNPkHnokF1iEkKULpLgrWzV6VW4O7nTNKT0rP0e1roy51Mymb87ptj3MGVmcuqpp0maMYPAxx8n5LVXUYU5Oa5WL6jVB5Z/APFl8+Thu2rdxZi2Y9gcu5mHFj1EUmaS3WK5lOirLl5M4BOPk7p2HUf63caZl14m65SsoxfiZiYJ3spWn15Ny7CWuDi62DuUy9pXD6JKoCc/rjlWrPKmjAxOjRpFyj//EPL6awQ9/ljRTkjr+SE4OMLc56CMHnbUt2pf/tfhf+yP3899C+7jXNo5u8bj6OVJ0GOPUXXJYgKGDyd53jwO9+zJ2ffeJ+f8ebvGJoSwD0nwVnTq4ilOp5ymdVhre4fyHw4OiuFtoth+MpHtJxOLVNaUkcGpRx8jdd16wsaOIWDo0KIH4BsOnV6Hw0th59Sily8lOkZ25OsuX3Mm5Qz3zr+Xo0n275Fw8vcn5MUXqLpoIX79+1/eMOfcp5+Se/GivcMTQtiQJHgr2hCzAYCWYS3tHMm1bm9aCS9XJyatPVboMqbMTE49/gSp69YR9v77+PXvX/wAWjwEES1h/guXD6Mpi1qEtWBi94mk56QzbP4wix9SU1zOoaGEvfsOVebMxrvDrVz4+hsOd+nKhZ9+wiSH2ghxU5AEb0UbYjYQ5B5EFd8q9g7lGl6uTtzRtBJzdp7h3MWCj5HVWVmceuIJUlevJuy9d/EbOKBkATg4wm1fQU6WMau+jHbVA9QLrMevvX7F39WfEQtHWHX/+qJyjY4m/OOPif7rT9zq1uXcuA840qs3yfPm2WzTHiGEfUiCtxKtNRvObqBFWIuijU/b0L2tK5Odq/ltw42XzGmTiTMvvUzqylWEvvM2frffbpkAAqtB5zfg4ELYMcUy97STCO8Ifun5C3Uq1OH5Fc8z6d9JpSqButWpQ+QPE4n4/nscPD05/exzHBs8hLRNm+wdmhDCSiTBW8nBxIPEZ8TTMrT0dc9fUiXIi441g/hl3XHSs66/P73WmtgxY0meN4/g55/Df/BgywbR8hGIbAPzX4Kksj3r28/Nj++6fUeXyl0Yv3k84zaOI9dk3X3/i8qr7S1E//UnYWPGkHPuHMeH3cvJRx8j88gRe4cmhLAwSfBWcmn8vVVYKztHcmOjOlTjQmoWf2y5/ilzF779loRffyXgvvsIePBBywfg4AC3fQG5WTD7yTLdVQ/g5uTG+FvHc2+de/lt3288u/xZ0nPS7R3WfyhHR/wGDqDqgvkEPfMMaRs2cKRvP2Leektm3AtRjtgswSulJiql1imlXrvBNSFKqVVFLVcabYzZSKR3JGFeYfYO5YaaR/nTtLI/3644Qnbufze+SfjjD+I++RSffn0JfmG09YYaKlSFrm/DoSXGVrZlnINyYHTz0bzU4iWWnVzGiIUjiM+It3dY13Bwdydw5MNUXbwI/zvvJHH6nxzu1p24L7/ElGa5rYyFEPZhkwSvlBoIOGqtWwNVlFLVr3ONPzAJ8CxKudIox5TD5tjNpXL2/NWUUoy6tSqnE9OZu/PKbPaUNWs4+9bbeLZrR8X33y/cJjYl0fwhqNoJFr4K5/ZZty4bGVp7qLFWPmE/Q+cO5UhS6ewGdwoIIPT116gy+28827bl/OdfcLh7DxL++AOdW7qGGIQQhWerFnwHYJr59SLgevu25gJDgOQilit19l7YS0p2Ci3CWtg7lELpVCuYGiFefL38MCaTJvPIEU4//QyuVasS/r//oZydrR+EgwP0/wZcPOHPEZBd8Mz+sqBz5c5M7D6RtJw07pl7D2tPr7V3SPlyjY6m0mefUvm333AOD+fs629wtH9/UlasKFUTBoUQhWOrBO8JXJpBFQ+EXH2B1jpZa331np8FllNKPayU2qyU2hwXF2fBkItv67mtADQLaWbnSArHwUHxyK1V2R97keWbDnLykVEoFxcivv4KRy/Pgm9gKd4h0P8riN1V5o6VvZGGQQ2Z0nsKoV6hPLr0UX7b+5u9Q7ohjyaNqTzlN8I//RRTVhYnRz7CiQceIGPPHnuHJoQoAlsl+BTA3fzaqwj1FlhOaz1Ba91Ma90sKCioxIFawpbYLUR6RxLoHmjvUAqtb8OKVPZxJv3l0eScPUvEl1/gHB5u+0BqdIcWI2H9V3Bwse3rt5KKXhX5pecvtAtvx9iNY3lv/Xtkm0rviXpKKXy6d6Pq7NmEvPoqmXv3cfT2Ozjz4ktkx5TdjYmEuJnYKsFv4Ur3ekPgmJXL2Y1Jm9h2bhtNQprYO5QicXZ04P2TC6ly5gDnH30B90aN7BdM13cguC7MeAQuxtovDgvzdPbkk46fcH/d+5m6fyqPLnnUrgfVFIZycSFg2D1UXbSQCiMeJHn+fA736Mm5//tYtr4VopSzVYKfCQxTSn0MDAbWKKVeKka5uVaL0EKOJh0lMTORJsFlK8EnTp9OhWXzWNCwO+9nRmIy2XHM1dkN7pgIWakw/QHIzbFfLBbm6ODIs82e5Z0277A5djP3zLuH48nH7R1WgRx9fAh+7jmqzp+Hd/duXPjuOw5360785Mno7NLbEyHEzcwmCV5rnYwxYW490FFrfVxrPS6fazvcoFzpbu5gdM8Dpep42IKk7/6Xs++8i2eb1kS98Ax7Y5KZv/usfYMKrg19P4Hjq+Gfd+0bixUMqD6A77t9T2JmInfPvZv1MevtHVKhOIeHE/7hh0RNn45rjRrEvvseR/r2I3nxYpmIJ0QpY7N18FrrBK31NK11kTJHccvZy9ZzWwl0DyTCO8LeoRRKTkICp598EsfAClT8v/+jX+NIqgV78b8lB8i1ZyseoOGd0PR+WPMJ7Jtn31isoGlIU37r/RtB7kGMXDyy1G1veyPu9eoS+dOPVPrma3B05PQTT3L8nmGk79hh79CEEGayk52FbY3dSuPgxqV2//m8dG4uZ54fTU5cHJU+/RQnf38cHRTPdKnBoXMpzNpeCraO7TEOwhoZ4/HxpXMdeUlEeEcwufdkOkV0Yvzm8by48kXSssvGJjNKKbw7dKDKrJmEvv02WcePc2zInZx65hmyTl5/Z0QhhO1IgregmJQYYlJjykz3/PkvvyJ1zRpCXn8N9/r1L7/fs14o9cJ9GL9wPxnZdt7oxNkNBv8MSsHUeyG7dG37agmezp583OFjnmryFAuOLWDY/GGcvFh2EqRycsJ/yGCqLlhA4KOPkrJ8BYd79SZ27DhyExPtHZ4QNy1J8BZ0af17WZhgl7p+A+e//hrf/v3xGzToP585OChe7VWHM0kZTFx91E4R5uFfGQZ+B7G74e8nyvx+9dejlGJE/RF81eUrYlJjuHPOnaw5vcbeYRWJo5cnQU8+QdUFC/C9rR/xv/zCoW7dufDDj3IGvRB2IAnegraf246Hkwc1/GvYO5QbyklI4MwLL+ASFUXo669ddzihddUKdK0TwlfLDhF3MdMOUV6lRjfo/Drs+gNWf2zvaKymbXhbpvaeSohnCKOWjOL7Xd+XmXH5S5xDgqn43ntEz5iBe8OGnPvwQ4707EXS3Lll7ncRoiyTBG9BO8/vpH5gfRwdHO0dSr601sS8/Aq5CQmEf/x/OHjmv1Pdyz1rkZlj4uPFB2wY4Q20fRbqD4Kl78C+Ur9istgifCL4teevdI/qzqdbP+XpZU+TnJVccMFSxq1mDSK/m0DExO9x8PbmzHPPyxn0QtiQJHgLycjJ4ED8AeoH1S/4YjtK+OVXUpYvJ3j0aNxq177htVWCvLinVWWmbjrB/rOlYFMTpaDf51CxCfz5EJzdbe+IrMbD2YMP23/I882eZ+WplQyePZh/L/xr77CKxeuWW4j+czphY8deOYP+scfJPFIKhn+EKMckwVvI3vi95OgcGgQ2sHco+crYs4dzH32EV8eO+A+7p1BlnupcHW83Z96Ytbt0dK86u8Odv4GbD0y5C1JKx/kD1qCUYnjd4fzY40dyTDkMmzeMKfumlI7/DkWkHB3xG9DfOIP+6adJW7+eI337cvadd8i5cMHe4QlRLkmCt5CdcTsBSm0L3pSezunnnsfR35+wMe8Xehmfv6cLL/aoxYaj8cwsDcvmAHzC4M7JkHoOpgwxdrwrxxoFN2J63+m0CmvFmA1jGL1yNClZKfYOq1gc3N0JfGQkVRctxH/IEBKmTuNwt+6c/+ZbTOnlb4WEEPYkCd5CdsbtJNwrvNQeMHNu/P+RdfQoFT/8ACd//yKVvbN5BI0i/Hh/7l6S0kvJtqThTeH2iXBmW7nbzvZ6/Nz8+KLzFzzd5GmWHF/CnXPvZH/8fnuHVWxOFSoQ+sbrVJk9G49WrYj75BMO9+hJ4p9/oXPK939LIWxFEryFXJpgVxqlrl1LwuTJBAy/F89WrYpc3sFB8V7/esSnZvF/i0pRUqndB3p+CAcWwLznyuXyubwclAMP1n+Qid0nkp6dztB5Q5m2f1qZ7LK/xLVKNBFffkHlX37GKSSEmFdf5cht/UleuKhM/15ClAaS4C3gXNo5zqaepUFQ6Rt/z01O5swrr+JSpQpBzzxT7PvUC/fl3tZR/LL+ONtPJlouwJJq8RC0fQa2/AQrx9s7GptoGtKUaX2n0SykGe+uf5enlj1FQkaCvcMqEY/mzYma+jvhn30KwOmnnuLYoMGkrFkjiV6IYpIEbwG74nYBlMoEH/v+++TExVHxgw9wcHMr0b2e61aDUB83Rv+xw/473OXV+U1oMASWvQdbf7Z3NDZRwb0CX3X5iheav8Dq06u5/e/bWXtmrb3DKhGlFD7dulHl71mEjRlDTvwFTj44ghP33U/69u32Dk+IMkcSvAXsPL8TJwcnagXUsnco/5G8aBFJs/4m8JFHcK9fr8T383ZzZuzA+hw8l8JnSw9aIEILUQr6fQFVO8PfT8Ku6faOyCYclAPD6gxjSu8p+Lj4MHLxSMZvGk9WbtneNU45OuI3cABVFywg5JVXyDx4kGN33sXJxx4n40Ap2ZNBiDJAErwF7IzbSS3/Wrg6uto7lMtyzp/n7Jtv4Va3LoGPjLTYfTvUDGZws0p8s+IwO0pTV72TCwz5FSq3gRkjy+Xpc/mpGVCTKX2mMKTmECbtmcTQeUM5klj2D+ZxcHEh4N5hVFu8iKCnniRtwwaO3taf0y+8IIfZCFEIkuBLyKRN7I3fS93AuvYO5T/Ovv0OptRUKn4wDuXsbNF7v9anDiE+bjxf2rrqXTzg7qkQ1hD+GA6H/7F3RDbj7uTOa61e47OOnxGbGsuQOUOYvHcyJm2yd2gl5uDpSeCoUVRdvIgKDz7AxYWLONyrN2ffeYfs2HP2Dk+IUksSfAmdSD5BanYqdSuUngR/cckSLi5eTODjj+NarZrF7+/j5swYc1d9qdnG9hJXbxg6HQJrwJS74XjZHpcuqo6RHfmz3580C23GuI3jeHDhg2XqZLobcfL3J/j556m6aBF+tw8kYdofHO7albPvjyH7nCR6Ia4mCb6E9sbvBaB2hRtv+2oruSkpnH33PVxr1qTC/fdZrZ6ONYMZ2jKSCSuPsOJAKdtNziMAhs0E30oweRAcK1unspVUkEcQX3X+infavMPe+L3c/vftZX45XV7OIcGEvfUWVefPw6dvHxJ++43DXbtxdowkeiHykgRfQnsu7MHFwYWqflXtHQoAcZ98Ss65c4S987bFu+av9nqfOtQI8eK5adtLx4lzeXkFwX1zwKciTL4Djiy3d0Q2pZRiQPUBzOg3g4ZBDXl3/buMXDySs6ln7R2axbhERFDx/feNRN+7NwmTjUQfO3YcOXGl7KFTCDuQBF9Cey7soYZ/DZwdrJtMCyN9504SJk/G/+67cW/Y0Or1uTk78vldTbiYkcOz07ZjMpWyFqJ3KNw3F/yj4LchcGiJvSOyuTCvMCZ0ncDrrV5ne9x2BswawF8H/yo3rXkAl8hIKo55n6rz5uLTs6dxDn3XbsSO+4Cc8+ftHZ4QdiMJvgS01uy9sLdUdM/r7GxiXn8Dp+Bggp552mb11gz15vU+dVh18DwTVpXCmdtewTB8DgRWNw6n2T/f3hHZnFKKwTUH82e/P6kVUIs3177Jg4se5HjycXuHZlEulStTcdxYI9F37078zz9zqEtXYj/4UA60ETclSfAlcOriKS5mX6ROhTr2DoX4SZPI3L+fkNdexdHLy6Z1D20ZSa/6oXy4YB9rD5XCFpNnBRg+G0LqwdR7YOcf9o7ILiK8I5jYfSJvtH6DfRf2MXDWQL7b+R3ZuaXkfAELcYmKouIH46gydw4+3bsRP2kShzp3MSbjxcTYOzwhbEYSfAn8G2+cz23vBJ918iRxX3yJV5fO+HTtavP6lVJ8eEdDqgZ58dhvWzmVkGbzGArk7g/3zoSIVvDXCFj3pb0jsgsH5cCgGoOY1X8Wt0bcymfbPmPwnMHsiNth79AszjU6mooffGAk+l69SJgyhUNdu3Hm1VfJPCpn0YvyTxJ8Cey9sBcnByeq+Vl+KVphaa05+9bbKEdHQl97zW5xeLk68e2wpuTkakb+sqV0rY+/xM0X7vkTaveDha/AotfBVPbXiRdHkEcQH3f4mM86fsbFrIsMmzeMMRvGlNljaG/ENTqaimPep9qihfjfeSfJc+ZypFdvTj3zDBn79tk7PCGsRhJ8Cey5sIfqftVxcXSxWwzJc+aSumYNQc88g3NoqN3iAKgS5MUndzbi3zPJvPTnztI5kcvZDQb9BM1HwNrPYOYoKGdd1EXRMbIjs/rP4u7ad/P7vt/pO7Mvsw/PLp3/7UrIuWJFQl97lWpLl1DhoYdIXbWao/0HcHLkI6Rt3Wbv8ISwOEnwxaS1Zm/8Xrt2z+cmJhI7dixuDRvgf9eddosjr861Q3i2aw1mbj/Dp6Vpv/q8HByh13jo+Brs/N1YRpdetk9jKwlPZ09eavESv/X+jVCPUF5Z/Qr3LbivTJ83fyNOgYEEP/sM1f5ZStDTT5G+cyfH776b48PuJWXFCvRN2qsjyh9J8MV0JvUMSZlJdk3wsR99RG5SEmHvvINydLRbHFd7olM1bm9SiU+WHGT6llP2Duf6lIJbR0P/r42NcL7vAhcO2zsqu6oXWI/JvSfzVuu3OJJ0hMFzBjN2w1iSs5LtHZpVOPr4EPjII1RbuoSQV14m6+RJTo58hCP9+pE4fTqmzFK2t4MQRSQJvpj2XjB2sLNXgk/duJGkP/+iwgP341azpl1iyI9SirED69OmagVe+nMna0rjzPpLGt1tzLBPT4DvOsHRlfaOyK4clAO317idOQPmMKjGIH7f/zt9Z/RlxsEZ5WJf++tx8PAg4N57qbZ4ERU/+hDl7ELMa69zqHMXzn/9NTkJN2/vjijbVHkaa2vWrJnevHmzTer6YtsXfLfrOzbcvQE3p5Kds15UpsxMjvYfgM7Opsrsv3Fwd7dp/YWVlJ7NoG/WEpOYwbRHWlM7zMfeIeUv/ihMuRMuHIKeH0KzB4xW/k1u74W9vL/hfXbE7aB2QG2eb/Y8LcJa2Dssq9Jak7Z+PRd+/JHUlatQbm74DRxAwPDhuFSubO/whLiGUmqL1rrZ1e9LC76YDiQcIMonyubJHeDCtxPIOnqU0LfeKrXJHcDX3Zkf72+Bp6sTwyZu4EhcKZ6hHRANDy6GKh1h7rMw63HITrd3VHZXu0Jtfu75M+PajSMxM5EHFz3IE0uf4EhSKdzUyEKUUni2bk3khAlUmf03Pr17kfjHdA736MmpJ54gbfPmcjkJUZQ/0oIvph5/9qBeYD3G3zreJvVdknn4MEf6D8CnRw/CP/rQpnUX16FzKQz5dh0uTg5MG9maiAAPe4eUP1MurPjA+AqtD4N/hoAq9o6qVMjIyWDy3sl8v+t70nPSuaPGHTza6FEC3ALsHZrVZZ87R8Lk30j4/XdMSUm41q5NwNC78enTBwc32z/kC5FXfi14SfDFkJqdSqvfWvFE4yd4uMHDVq/vEm0ycXzYvWQdOkSVeXNxqlDBZnWX1J4zydz13Xp83Z2ZNrI1ob6l/B/FA4vgr4dAaxj4LdTsae+ISo34jHi+3v41fxz4AzcnN0bUH8Hdte7Gw7kUP7hZiCktjaTZc0j49VcyDx7E0dcXv0F34H/XXTiHh9s7PHGTki56CzqYYCz/quFfw6b1Jk6fTvqWLQS/MLpMJXeAOhV9mPRACy6kZHL39+s5m5Rh75BurEY3GLkCAqKMsflFr0NOlr2jKhUC3AJ4tdWr/HXbXzQPac6nWz+l11+9mLx3Mlm55ftv5ODhgf+QwUT/PYvISZPwaNmSCz/+xKGu3Tj52OOkrlsn3fei1LBZgldKTVRKrVNK5bvd2tXXKKWclFInlFLLzV/1bRXvjRxIOADYNsHnxMVxbvz/4dGiBb4DB9qsXktqFOHHTw+04FxyJoO+XcvJ+FK4pW1e/lHwwCJjwt3az2BiVzh/yN5RlRpVfKvweefP+aXnL1Txq8K4jePoM6MPfx38ixxTjr3DsyqlFJ4tW1Dps0+ptmQxFUaMIH3rVk7c/wBH+vYl/rffyL140d5hipucTRK8Umog4Ki1bg1UUUpVL+Q1DYApWusO5q9dtoi3IAcSDuDl7EWYZ5jN6owdOxadnk7oW2+hyvDs7uZRAUwe0ZLk9BwGfbOOw6V54h0YO9/1+R8MmQyJx+HbdrBlktF1LwBoFNyIid0mMqHrBALdA3lz7Zv0n9WfeUfmlduldXk5h4UZG+csX0bY2LE4uLoR+867HGx/K2defZX0HTukVS/swiZj8Eqpz4AFWut5Sqk7AXet9Y8FXWP+egxIBXYBI7XWOVeVexh4GCAyMrLp8ePWPwJz+PzhAEzqOcnqdQGkrFzJyYdHEvjE4wQ99phN6rSk5LQsjsVdZP2BWGqF+9O+Thh7Y5IZNnEDAD/d34J64b52jrIQkmNgxkg4usLYz77P/8Az0N5RlSpaa5afXM5n2z7jUOIhqvpWZUSDEfSI6oGTg5O9w7MJrTUZu/8lcdo0kubORael4VqjBn6DB+Pbry+OPqV4uagok+w6yU4pNRH4TGu9QynVDWiitR5X0DXAUuCU1jpGKfUzMF1r/Xd+9dhikp3WmjZT2tC7Sm9ea2X9w11MaWkc6dMX5e5O9Iy/cHCx3773hXUwJol/dp3mWNxFjp27SEZ2Lp6uTsQlZ/BAp5oMucU4nOdwXArDvt9AYno2X97dhI61gu0ceSGYTLDuc1j6rnF4Ta+PoO4AWTN/FZM2sfDYQibsnMChxENEeEcwov4I+lbpi7Ojs73Ds5nclFSS584lcdo0Mv79F+Xmhk+PHvgNHox740ZlujdOlB72nmSXgtEaB/DKp97rXbNTa33pAOfNwDVd+7YWkxpDSnaKzcbf4z7/guwzZwh75+0ykdwBUjKy8fdyZUCLaN4a3IyqId54uTkTUcGTQW2qXr6uapAXMx67hehAT0b8vJnJG6zf+1JiDg5wy1PwyCrwi4Tp9xtnzF+MtXdkpYqDcqBndE/+7Pcnn3T8BG8Xb95c+ya9ZvRiyr4pZOSU8kmWFuLo5WlMyvtzOlHTp+N7221cXLSI43ffzZG+fbkwcSLZ587ZO0xRTtkqwW8B2ppfNwSOFfKaX5RSDZVSjkB/wO6HVttygl3Gnj3E//wzfoMG4dG0qdXrs5TG0YEMblMVpeCtaZtpFBWIo4Pivo41cbiqxRLi48a0ka1pVz2QV2fsZtz8fZhMZWC8Mri2sTFOl7fh4GL4sgXs+F3G5q/ioBzoHNmZ33v/ztddvibUI5QxG8bQ86+eTNw1kaTMJHuHaDPu9eoS9vZbVF+1ktB33sbRy5tzH43nUIeOnHj4YZLnzZP974VF2aqL3gdYhdHl3hPoAdyVt5v+Ote0AiKA3wAF/K21fvVG9diii37Czgl8vu1z1t21Di8XL6vVo3NzOTZ4CNmxsVSdOwdH3zIwRm2WnWvix3/2sXJPDC8OaExyWha/rTrIFyPa5tslmZNr4o2//+W3DSfoVCuY/w1phK97GenKjTsAsx6DUxshqp1xUl1wLXtHVSpprdkcu5kJOyewPmY97k7uDKg2gHvq3EOEd4S9w7O5zCNHSZo1i6RZs8g5exYHb298evXCt/9tuDeSLnxROHbf6EYp5Q90BVZqrc8W95obsUWCf37F8+w+v5sFty+waj3xkyYRO3Yc4R//Hz69elm1LkuKSUhj7F/b8PN04fl+DfFyd+bRCau4r2NNWtUIuWFZrTW/rD/OO7P3UMnfnW+HNaNmqLeNIi8hUy5s+QmWvg1ZqdD6MWj/Arha7yGwrNsXv4+f//2Z+UfnY8JE58jO3FvnXhoFN7J3aDanc3NJ27CBxJkzubhoMTojA5eoKHxv64dP7964REbaO0RRitk9wduCLRJ8v5n9iPKJ4rNOn1mtjuwzZzjcpy8ezZoS8e23ZeYpfuWeGL6Yv5s721ZjQIsolFIcikniq4X/8n/DWxf699h8LJ5Rk7eSmpnDB7c3oG/DilaO3IJS4mDJm7B9MviEQ/cxUOc2mYR3A7GpsUzZN4VpB6ZxMesiDYMaMrT2ULpEdrmpJuRdkpuSysWFC0maMYM0879nbvXr49O7Fz49e+IccuMHZXHzkQRvAZm5mbSY3IIR9UfwROMnrFKH1ppTox4ldcMGqsyejUul0r/9ZWZ2Lt8s2sO2o+d5ZWBjalT0+8/nuSaNo0PRElxscgaPTt7KluMJ3Nk8gjf61sHDpQwtszqxHuY+B7G7IbI1dHsPKl3z/z+RR1p2GjMOzeDXPb9yKuUUFdwqcHuN2xlUYxChnqH2Ds8uss+cIXn+ApLnziVjzx5QCo9mzfDp3Rvv7t1w8ve3d4iiFJAEbwH74/dzx+w7+LD9h/SMts7e5MkLFnL66acJfuEFKjxwv1XqsKQTcRcZ89c2Kgd582Tveni6Wq7FlZ1r4n+LD/D1isNEV/Dks7sal4318pfk5sC2X2DZ+5AaB/Vuh85vGDvkiXyZtIk1p9cwdf9UVp5aiVKKjhEdGVJzCC3DWuKgbs4dtjOPHCV53jyS584l6+hRcHLCs01rfHr1wrtjxzI1T0dYliR4C5h/dD4vrHyB6X2nUzOgpsXvn3vxIkd69cYxKJDoadNQTqW3xaq1ZtGOU0xcuo/7O9WkR6MIqw0lrD18nmen7uBCaibPd6vJiHZVitwjYFeZF2HNZ7D2c9C50OJhaPcceJT/U9hK6tTFU0w/MJ2/Dv5FQmYCUT5R3FHjDvpU6UMF97J1HoOlaK3J3LeP5LlzSZo3j5wzMUayb9kS765d8e7cCaegIHuHKWxIErwFfLHtC77b9R0bh27E1dHV4vePeestEqf9QdS0abjXq2vx+1tKWmYOn83bxZHYZF4Z2ISoYOtPhEtIzeKlv3ay8N9YGkX48eEdDagRUkYm4F2SfAb+ed8Yn3fxhFajjMl47tLNWpCs3CwWHlvI1P1T2RG3AyflRPtK7RlQfQBtw9veNLvkXU2bTGTs3s3FxYtJXrSI7OMnQCncmzTBu2sXfLp2lVPubgKS4C3g2eXPciDhAHMGzLH4vdM2b+b4PcMIGD6ckJdfsvj9LeVgTBJj/tpKw8oVeKR7XdycHW1Wt9aav3ec4a2//yUlM4cnOlXnkVur4uJUxrpsz+01zpv/dwa4+kCrR41k7+5n78jKhMOJh5l5aCZ/H/6b+Ix4At0D6Vu1L/2r9aeKbxV7h2c3WmsyDx7k4uLFXFy8hMx9+wBwq1sX765d8OrYEdcaNcrMpF1ReJLgLaD/zP5E+ETweafPLXpfU2YmRwcMRGdmUmX23zh4lL5ztbXWzNp0jN9WHeLR7nXpUM9+M9vPp2Ty9uw9zN5xhlqh3rzdry4tq5TB7tqzu2HFONg729j2tsVIo/veS7pXCyPblM3qU6uZcWgGK0+tJFfn0iCoAb2ie9E9qjuB7jf3OQFZx49zcckSLi5aTPoOY48wp7AwvDrcineHDni0bImDm5udoxSWIAm+hLJN2bT4tQXD6w7n6aZPW/TecZ99xvmvvibiu+/wate24AI2lpyexcd/7+T8xQxeHtiY8ABPe4cEwOI9sbz197+cTkynb8OKvNKrFmG+7gUXLG1idhot+n1zwMkNGt9jdN0H3Lyt0aI6n36eOYfnMOfIHPYn7MdBOdAqrBU9o3vSObIz3i5lbDjHwrLPnSN15UouLl9O6tp16LQ0lJsbnq1b49WhA14dbpXld2WYJPgSOpJ4hNtm3caYtmPoW7Wvxe6bsf8AR2+/Hd/evaj4wQcWu6+l/HsynnEzttO2VigPdK6Fs2Pp6g5Pz8rl6xWH+WbFYRyV4vFO1XiwbbRNhw4sJu6AcZDNjt/BlGOsn2/zJIQ3sXdkZcqhhEPMOzqPeUfncTrlNC4OLtwacSs9o3vSLrwdbk43d6vVlJlJ2sZNpKxYQcqyZWSfPg2Aa+3aeLVti+ctt+DepHGZOftCSIIvscXHF/Ps8mf5vc/v1K1gmQlwOjeXY3ffTfaJk1SZN7dUrWk1ac3UNYeZtfEYT/epX+AudPZ2Mj6N9+fuZcG/ZwnzdePpLtW5vUklnErZA0mhJMfAhm9g8w+QmQyVmkPzh6Buf3Cy/OTO8kprza7zu5h3dB4Lji7gQsYF3J3caRveli6RXWhfqb1Vt5suC7TWZB0+TMry5aQsX0Ha9u2Qk4Nyd8ejeTM827TB65ZbcKlWTcbuSzFJ8CX07Y5v+WL7F2y4ewMezpYZI4//5Vdi33+fih99iG9fy/UKlFR8SgYfztxBdq6JlwY0Isin7HR7rzt8gQ8W7GP7yUSqBHkyultNetQLLZv/OGUkw/bfYNN3cOEQeARC0+HQ9H7wu/n2bS+JHFMOm85uYumJpSw9sZTz6edxdnCmVVgrulTuQoeIDgS4ybLF3JRU0jZuJHXtWlLXrDHW2wNOwcF4tmmD5y1t8GzdGqfAm3t+Q2kjCb6EXlj5AjvO7WDhHQstcr/L29E2bUrEhNKzHe2WI3GMn7WDHo0juKd9dRwdyl4LWGvNoj2xfLRwP4fOpVC3og+PdaxG97qhZWv9/CUmExxdDhu/hwPzjfdq9IBGQ6FGd7gJt3MtCZM2sTNuJ0uOL2HJiSWcTjmNg3KgSXATOkR0oF2ldkT7RJea/0/aU/aZM6SuXUvKmjWkrV1HbpJx+p9L1ap4tGiOZ/PmeDRvLuvu7UwSfAnd8fcdBHkE8XWXr0t8L601Jx8cQdr27VT5++9Ssx3t6fhUXvh5PaNva0ij6LL/hJ5r0szYdpqvlh3iyPlUqgR58miHatzWqGKpm0tQaIknYPOPxlr6lFijVd9gCDS6G0Lr2Tu6Mkdrzf6E/Sw5voSlJ5ZyKPEQAOFe4bQLb0e7Su1oEdriph+3B2NIMWPPXlLXryNt0ybSN2/BlJYGgEt0NB4tWuDRwkj4zsHBdo725iIJvgRyTbm0mNyCu2rdxfPNny/x/RJ+/52zb71N6Ftv4n/nnRaI0DK01mi45sz2si7XpJm/O4Yvlx1mb0wy4X7u3NcmisHNIvD1KKOt39wcOLwUtv0K++eDKRvCGkLDu42xeu+bc+/2kopJiWHV6VWsOrWKDWc3kJ6TjqujKy1CW9CuUjvaVGxDpHektO4BnZNDxt69pG3cSNrGTaRt2YIpJQUAl6goPJo3w71RY9wbN8IlWnpErEkSfAmcSD5B7xm9eafNOwyoPqBE98o6cYIj/Qfg0agRERO/l//R25DWmuX74/h6+WE2HovH3dmRAU3Cua9NVNnbFS+v1Auw6w/Y/iuc3QUoqHwL1BsAtW+TdfXFlJmbyZazW1h1ehUrT63kxMUTAIR6htIytCWtKraiZWhLgjzk7wvmFv7efUbC37SJtK1bMZm79B19fXFv1Aj3xo2MpF+/Hg6epWO5bXkgCb4Elp9czhP/PMGvvX6lYVDDYt9H5+ZyfPhwMvcfoMrfs3AOC7NckKJI/j2TxKS1x5i1/QyZOSbaVK3AnS0i6VYnpGwusbvk3D5jh7zdf8KFg6AcIbod1B0INXuCl3SdFtfx5OOsP7OeDWc3sPHsRpIyjeRV1bcqLcNa0jKsJc1Cm+Hj4mPnSEsHbTKRdewY6du2kb59O2nbtpF16LDxoYMDrrVq4tGoEe6NGuFWrz4uUZVRZXDOT2kgCb4EJu6ayCdbP2HtXWtLtGHGhR9/4twHHxA2dix+A/oDcDYxjeGfL2Ph670tFK1tJKVl8cTE1Xw4rBWhfqVv573CSkjN4vdNJ/l1/XFOJ6bj4+ZE/8bhDGoaQb1wn7Lbw6I1xP4L//4Fu/+ChKOAMpbc1ewJNXtBUE05p76YTNrEvvh9bIjZwIaYDWw9t5X0nHQUihr+NWgc3JimIU1pHNyYEM/SvcTUlnKTkkjfufNy0k/fvuPyOL6DpydudeviVq8e7vWM784R1jvEqjyRBF8Cr65+lXVn1vHP4H+KfY/Mgwc5evsdeLZtS6Uvv7j8P9qymOCT0rJ44/dN7DudyKQnOpbpBH+JyaRZd+QC0zafZMHus2TmmKgV6s2AxuH0qh9GREAZ/h21hrM7Yf8C2D8PYrYb7/tHGYm+RneIaAXOMpGsuLJys9gRt4PNsZvZFruNHXE7SMsxEle4VzhNgpvQOKQxTYKbEO0bfdMeeXs1nZtL5qHDZOzeTca/u0nf/S+Z+/ahs7IAcPDxMZJ93Xq41auHW+1aOFeqJC39q0iCL4Gh84bi5ujGxO4Ti1XelJHBsUGDyIlPoMrMGf9ZUlIaE/wTE1dz+kLqNe8/2qMuXRpU4sVf19O6RghfL9xTbhJ8Xknp2czecYbpW06x/WQiAA0j/OjbIIxe9cOo6Fd29gW4ruQzcGCBMTnvyArIzQQnd6jcBqp2hCodIaSutO5LIMeUw/6E/WyL3cbWc1vZGruVCxkXAPB29qZuYF3qB9anXmA96gfWl3H8PHRWFpmHDpG+ezcZu/81kv+BA5CTA4CDhweuNWviWrMGbrVqGa+r18DR6+Yd05cEXwJtf29Lt8rdeKP1G8UqH/PWWyT+PvXyXvPrD8TyzaI9pGZkM7hNVb5fuo+Fr/fmYEwSXy7YzfG4FOpF+PNcv4b4eRo7lx07d5FxM7YRl5xO5/qV2Hb0PH2aRnJbi2hG/7yOrg0rkZKRw8wNR3m4a23a1jbG97ccieO7xXs5l5ROqxohPNm7/uUx5vw+O5+cQY7JdM3v4evhgruLE2cT0gj196D7u3PLZYLP62R8GnN3xTBn5xl2n04GoHGkH11qh9C5djA1Q7zLdhdiZgocWw1HlsHhZXB+v/G+ZzBU6QBVboXI1sa++GX597QzrTUnL55kS+wWdp/fza7zuziYcJAcbSStEI+Q/yT82hVq3/T75+dlyswk88ABMvbtI3PffjL37ydj/35MFy9evsY5MhK3mjVwrVkL15o1cK1WDZeICJRT+T9KWBJ8MSVmJNJuajueb/Y8w+sOL3L55AULOf300wQ8+AAho0eTkJLJ8C+W8VCX2jSpEsiHM7ez73Qif43uxv1fLqd3k0h6Nonki/m7cXZ04PVBTQF45se1NK8WRMvqITw3aS1vDGpG9TBfvN2dGf3zOrJzTXi4ODGgZTTVw3zx83QlJiGNh75ewSPd69C0ShBj/txK/coBPNy1zg0/K6ybIcHndex8KnN3xbBg91l2nTYmWIX7udOpVjCdagfTukqFsj1BDyDp9JVkf2Q5pJ033vcKhchWRis/srXRwnco47+rnWXkZLAvfh+7zu9i1/ld7D6/m5MXT17+PNwrnJr+NakVUIuaAcb3MM+wsv1AaUFaa3LOnCFj/wEy9+8zvu/bR9bx48awFKCcnXGJisKlalVcq1bFtWoVXKpWwyU6qlzttZ9fgi//jzYldCz5GABRPlFFLpt16jQxr7+OW4MGBD/1FACbD8cR5ONG32aVAbinfXVem7KJDQfPATCsQw0clGJwm6q8PHkDuSaNo4Pi8NkknuvXgEoVvIgK8iYpLRNv9ytruFMzcvjo3tb/2cBl2e7TVA7yok9To67+LaKYvOoQD3etc8PPxPVFBXryWMdqPNaxGueSM1i2/xxL955j+pZT/LL+OC5ODjSr7E+bqhVoUy2QBuG+ZW8vfN9w4zS7xvcYO+jF7YMTa+HEeji+DvbMNK5z9YWIFsakvfCmxoE4HrLVa1G4ObnRKLgRjYIbXX4vMSOR3Rd2sy9+H/vi97E/fj/LTi7D2KECvF28Lyf9/2/v3KPrquo8/vndc859Jjc3z6ZJm/RBqZZSFCyPJTpFmI4s0FlLGZgZZRwcRccBR1ziC9FxRkdlGAd1wYwgiA+E8bF84wg4UwQFFYpiodA2IUmbpG3eNzf3fe6eP/a5N7lp2qQlD3qzP2vttffZj3P3Se7d333247dPrT2VU2KnsC62joiz/IanRQSntRWntZXq111Qii8kk2T27SPT0Um2s0PP8e9+lvEHHtDfaQCfD//q1SXh969Zg39NO/72dqz6+orpRBmBn4XueDcA7dH24ypXSKU4cO21oBSt/34z4vUWhxNpmqYcaVp8+x2IpxlP5bjs3x4AdAc0my8wlsxQVxWkpS7C7gOjRMN+eocnaGsoH7679FXtR1hnGxxP03V4nDfdpM3rugWFW1Czps02B2+ApmiQK7a2ccXWNtI5l8c7h3h07yC/6hji5gf2wAN7qArYnLO2jvPW17N1TR2bWqInlwU9nw9WbNJu6zt03GiPFvqeX2t/30PgiQ+1a6DlTC32rWdpwzv+5Sc8L4ZYMMb5redzfuvksdHJXJK9o3t5fvj5kuh/d893SbvpUp6VkZWsi61jfc161sfWs65mHeti65bllj1fOExoyxZCW7aUxRcyGbJdXWT27SPb0Ummo4NsZweJRx6BXG6yfCSC096Gv00LvnZtJ6X4G4Gfhe54N5ZYtFbP3ZysUor+Gz9O5rnnWPWft+FfPXkwSCwSYHg8U7oeiOsfaWM0yPrmKB+7bPJo0Il0juqQ7hi0NVRx28+f4ZafPM0bt65hfXP5DzfkP3K4tKE6yNZTmnj3n23y6gXJTH7WtE/8xauOOgdvOJKgY7FtYxPbNuo95kOJDI93DvOrjkF+vW+QXzx32MvnY8uqGGe21XJWey1ntsWorzrJToeLtWl3xhX6Oh3Xq/J7d0Lvk3Dgd3prHoD4oG69Hs5v3gwrPFezysznHwdhJ8wZjWeU2eBwCy494z10jnXSOdpJx1gHHaMdPHHwCTLuZPvSFGpiXWwd7dF22qrbtB9tY1XVKpxldoaBLxAguHEjwY0by+JVPk+ur49sdzfZrm6yPT1ku7v0W/+DD4LrTt6jKP6rVpdGD5zWFu23tL7kFvoZgZ+FrngXq6pX4fjm/mMYvvtrxH/yExrf9z6qt20rSztzXQNfun8XP//9fra01/PNX+4B4JwNTdzx0G52Hxhhc1sdj+w+yDd27OHe91/EwNgEu/YP8/m3nUc4YNMwx9PdXre5lR/8tosDQxO0NVTxoye6ePS5g9x9zQXHTGuImu1SL4b6qgCXbFnJJVv0Qsf+sRQ7u0fZ2TPCk90j3PloJ//1sH7rbasLs7k1ymktNZzWEmVzaw0NJ5PoB6Ow9rXaFUkc1oLf9xQc2qU7AMWhfYBgjSf2p0HTy6HhVO0ijUb454jls1hbs5a1NWu5sO3CUrxbcOlL9JUEv3Osk47RDu7vvJ/x3OSCNJ/4aIm00BZtKxP+1dWraalqIWCdRN/BF4nYNv62NvxtbfCa15SlqVxuBvHvJrNvH4mHH0ZlMmX5rVhsivBP6QC0tOK0rMSqXtyFk2aR3Sy8+UdvpjnSzK0X3jqn/OMPPcSB9/4j1RddROsXbplxOOeR3f185aHdZPMFLjy9le881jm5iv5nu+g8PM7q+gjv2r6JLe31FJTimjse5XA8xUQ6jwicfUoTN1x2Jo7lK62i337GkUeIPtkxwB0P7aZvJMkpzVGuvXgza1dEZ02bC8ttkd18kc65/LF3jCe7R3j6wCi7euP0DCdL6c3RIKe1RDmtJcqGFdWcuqKaNQ1hAvZJvKgtHYfDu+HQH7UBnoO74PCzkE1M5gnWTIp9w4bJcKwdbDN69GJQSjGaGaU73k3PeA89ce26x7vpifeQyCXK8jeEGmipaqEl0lLmt1a1srJqJSH7JN8qOg8opXCHhsj19pLr7SXr+bkDvaW44n7+Ir5IBHtlM2133TWvB/KYVfQnQEEVOOeec7h84+Vcv/X6WfMnd+6k56q3E9i4kfa7v4ovPD/C9z9P9fDws/1cd+kWgn6LvuEkH7/vd9x05bmsaTJbaSqBsVSOZ/viPNM3xjN9cXb1jtExkMBbFoHlE9rrw5zaVM2GFVWc0qRde32EqsBJOhBXKEC8Fwb3wOBe7Q/t1eHx/sl84oPoKqht1/P8JbdW++E68+b/IlBKMZIZoSfew/7x/fQl+uib6NO+F84X8mVl6oJ1rIyspDnSTFO4iaZwEyvCK2gMN5bCy3Hh31RUoTDZAejrI9d/kNzBg+QP9tNy8834AvM3SmIE/gToT/Sz/XvbufHcG7l84+XHzJvZu5eut16JHYvRfu+3sOvmb0XxwZEkt/z0j+zpGyWTc6mPBrno9FVc+ScbTqoFH4bjI51z6RyYYO/hcfYeSpT8rqGJkvADNFQFaK8Pa1cXYU1DmLa6MGvqI8TCzsn5HUnHtdgP7NFmdke6Jl3iUHlef7UW+ppVehdAtEV3CKIt+rq6xVjpexEUVIHB1GCZ4PcmeulL9HFo4hCHk4fLhv+LRJyIFv9QU6kT0BhupD5UT33Qc6F6ov6T2CT0SwQj8CfAY32PcfWDV3Pn9js5e+XZR82Xfn4PPVddhVgW7d+6p2xRncEw32TyLi8MTtBxeILu4Qm6B5N0DU3QM5ykfyxdljfit2iJhVgZC9EaC7KyJsTKmiCtXtzKmuDJt3c/O6FX808V/eEX9GhAvBdSI0eWCTd4gr8Kqlfq43QjjVC1Qh/AU9WkjfuYjsAJkcwlGUgNcDh5mENJLfpFV7weTA6WDPtMxRabumAddaE66oP11AXrqA+V+7WBWqKBKLFAjCqnynQIpmH2wZ8Ac9kil9r1DPvf+U7EcWj72t1G3A0LTsC2eFlzlJc1H7leIp1z2T+cpGsoSffQBAdGUvSPpegfS/Ns3xiDiewRZeoifpqqAzRWB2is0n6D5zdOia8JOfh8L4GG1R/Ri/OaXj5zenYC4v0QP6DN8o71Tor/aA/0PDZzJwD0/v4qT/gjjZ7wN0KoVk8FhOrKfSdspgfQK/3bnfZjtpUFVWA4PVxyQ6mhcj89xHBqmM6xToZSQ2QLR35XASyxqAnUaOevIRaIlcS/JlBT8ovpVf4qqp1qIv7IcS2WrgSMwB+D7ng3ITtEU3jmxRDxBx+k74Mfwq6tpe2rd+FvP7698gbDfBN0LDasqGbDUc63T+dcDo6l6RtL0T+apm80Rd9YmsFEhoHxDJ0DEwwkMmTzR26TtH1CfZWf2rCfmpBDbdhPbcQhFvZTGy76U8MONSFn8Y39+CPQcIp2RyOfhYkBPdxf9BOHtZvw/EPPaIt+3rGwM2IFpgl/7aQfiOpdBoEaz4+W+/5qbWtgmeATHw2hBhpCDbPmVUqRzCcZSg0xlB5iND3KWHaMsYx2o5lRRjOjxDNx+if62T28m3g2TiqfOuZ9Q3aIKqeKiBOh2l9NlVOlOwBTw051mR+2w4SdcMkP2SEc38kx9WUE/hh0xbtoj7Yf8Y9UuRwDt97K0JdvJ7jldFbfeit2w+xfWoNhqQk6FmsaIqxpOPoCKKUU45k8A+OZcpfIMJTIMJLMMZrMsm8gwWh3ltFkjnzh6FN9IceiOmhTHbSpCjpEi+GATXXQKYWjxXDQJuy3Cfstwn6LkN8i7LcJORbWfI0g2H49P18zB/sW+SykhiE5XO6nRqbEjWh/4PnJtMKRw9HlCASqZxD+iHaO5/vD4K/SowXFtKOl24GKGFEQESJOhIgToS3aNudyGTdT6gCMZcaIZ+KM58ZJZBMlP5FLMJ6dDPdP9JPIJUhkE2XGg46FLTYhJ1Qm+jN1BKaGQ3aIgBUgaAd5dcurCdoLPx20aAIvIncCm4CfKqU+Ndc8cym3UHTHu9lUX266NfnUUxz61KdJP/MMNW96E80fvxFf0MzbGSoHESEadIgGHdY3Vs2av9ghGJ3IMZLMMpLUoj+SzDKWypFI5xlP50lk8sTTORKZPP1jacbTOm0i6876GUUCts8Tfpug49PC73UEwn6LkKM7BgHbR8DxEbAt/LZPX9uT8X7LR8Dxru1p+ZzJvH7Lh8/26zn76ua5/xGVglwKMnG9YDATh/TYtOvp/pgeSchOQDbp+QlQc//7IJYWeicI9hRXdh0AJ6R9OzTztR2cjLP8YDmePyXsc2aOt/z6nIIl6GgErEBpQd+JkCvkmMhOlHUGUvkUyVySZD5JMpfU1zOEk/kkg6nBUjiV02nuDP+/HZfvqByBF5E3AZZS6jwRuUtENiil9s6WBzh9tnILRc7N0Zvo5eK1F6OyWSZ+81tG7ruPxC9+gdXYQOsXv0B0+/bFqIrB8JJmaoegrf74t4a6BUUik2c8nWPc6wwks3lSWZdk1iWZc0ll8ySz7mRc1iWVy5fCQ4ks+70yqZxLJl8gmy8cc2RhrvgEbMuH4xMc24ft8+FYgm0Jjs+HY/mwLSnlsS3Bsbx4n3jpFo7VgGM1Yvu8/D7B5xOskGBHvLB4vhe2BBzJ4y+kCRRS+AspAkr7jpvCKaTw51PYhRSOm8R209huCruQwedmsQppLDeDz81gpTP43DEkn8HnphE3gy+vfcmnEeZvwbVCpgi/jRzRCXB0B8Fne87ynF0eJ9a0PPa0fF5YjpFWlsfS2y6nOy/eER8xz5WnRyEQg2AxTvT9ZrjH1HSFkFMuSTdLWuVIFbKk3Sw1zuJsb16sN/htwLe98APA+cB0oZ4pzyvnUG5B6P7DI1z/3zlO+86PeH7/Xah0Gqu2loZrrqH+qr/FF1neezwNhvnC8gk1IT1fP9/k3QJZt0AmVyiJfiavOwCZvKvjS+nFeJ0vnXPJuQXyriJX8Hy3QM5V5F3dedDXxTxevKsYz+XJTymTLyjyriLrFkp58gWFqxSFgjqBjkjAc7F5+kspHFwCZAmS075kCZDDxsUhj1/yOBSdi78Yljz21Gsvzp+fmj+PX1xdzruPnzyW5LFwsSlgi4uFi0UBiwI25dfFsI2Lb9q1zXGMciwiAvg9N5XR9zxDrGnhz/VYLIGPAL1eeBg4c455Zi0nIlcDV3uXCRF5fp7q7LG7ARgsXT7+GFx7zfx+xEuD8uesXMxzVhbmOSuL5fGcn1w938854wrvxRL4BFC0bVgFzLR0dKY8s5ZTSt0O3D6flZ2KiDwx0/7CSsM8Z2VhnrOyMM9ZWSzWcy7WHo0n0cPrAGcAXXPMM5dyBoPBYDAYprFYb/A/AB4RkRbgYuD1IvJhpdRnj5HnXPRB09PjDAaDwWAwzMKivMErpeLoRXSPAxcopbqniftMecZmiluM+k5jwYb/X2KY56wszHNWFuY5K4tFec6KskVvMBgMBoNBs3zsJBoMBoPBsIwwAr+MEZEaEfmZiDwgIt8XkenbNSsKEVkhIk8tdT0WGhG5TUTesNT1WChEpFZE7heRJ0Tky0tdH8OJ4/0mH/HCFdseTX3OaXEL2h4ZgT8KInKniDwmIh9b6rosIG8BPq+U2g4cBF6/xPVZaG5mcttlRSIirwGalVI/Xuq6LCBXAvd424yqRaTitlVNF4RKbI9EpBb4GtreCVRoezTDcxZZ8PbICPwMTDWbC6zzzOZWHEqp25RSD3qXjcDhpazPQiIirwMm0A1HRSIiDnAH0CUif77U9VlAhoDNIhIDVgP7l7Y688t0Qajg9sgFrgDiUNHtUdlzwuK1R0bgZ2YbR5rIrVhE5DygVin1+FLXZSHwhvpuBD681HVZYP4GeBa4CThbRK5d4vosFI+iLXe9F9iNtnJZSUwXhG1UYHuklIrPtDOq0tqj6c+5mO2REfiZmW4id8US1mVBEZE64EvA25e6LgvIh4HblFKjS12RBeaVwO1KqYPAN4ELlrg+C8UngHcrpf4ZeA64aonrM6/MIHymPaosFq09MgI/M3MxrXvS4/UkvwN8RCnVvdT1WUAuAv5BRHYArxCRryxxfRaKfcA6L/wqoFL/p7XA6SJiAefAPB6D9tLEtEeVxaK1RxX5RZkHlouJ3L9DH+Bzg4jsEJErlrpCC4FS6rVKqW1KqW3A75VS71jqOi0QdwIXiMgvgfegF/FUIp9BGwoZA+qAe5e2OguOaY8qiMVsj4yhmxkQkSjwCPALPBO5S2RFz2AwLFNEZIdSaptpjwwnihH4o+CtZP1T4JfenKbBYDAsCaY9MpwIRuANBoPBYKhAzBy8wWAwGAwViBF4g8FgMBgqECPwBsMyRUTaRWRBTWWKiGljDIYlwvz4DIblyxuADxwtUUQuEZEbTvTmIrIeeHauZnNFxCcizSLSJCJnicjlIvIFEXm36SgYDMeP+dEYDBWMiKwTkTeIyL+KyFPeauwim4FREblZRK6boXgPcNaJfrZSqgN4BfC0iJwtIm8RkctExD5Gsf9DbwWLAE8Bh9BmPWtOtB4Gw3LlWD80g8Fw8uNHW3v7HhBQSo14tr7/Em085TfAnUqp3TOUHWXagR8iIsBbgYeUUv3TC3j3vhBoQVtdSwKXoI3uDKFfKmLA4PSySqmCiNzild+BPojjdOAapdTI8T22wWAwb/AGQ2WzF314STPwbRH5HDAO/Aj4PPANZjisxRPyVwKvFZGfi8gmz6TmDcAHObqt8N+iD0m5DmhXSr3bu/83gDXAfqXUEeI+hW969fOhjwv9g1Lq+8f1xAaDATBv8AZDRaOUcj0b3xvQ9sw/6flXAzm0edBPisiZSqk+T9g/in67rwF2Am9XSmVFZLNS6h0ici7wxaN85HnA2UqpL4rIIS/uBaXUsIjsBO4WkUuVUnuLBTxLbVGgAX2Qym/RHZIo4Pfe6huBVmCHUuqf5uevYzBUNkbgDYYKxpvvzqHfileih8dr0HbrrwceR4v4IQClLV992iv7v0CPUirr3a745p1QSo0f5SOvBP7ZC1uen/Hufb+I/ExNsa4lIlXoEYEg0A/sATqATrTgnwvsVEp9/cT+AgbD8sUM0RsMlU0QKKCHyMNom+YHlFJ/AF5Any+eAJyphUTk1V78+SLyQ+/NPucl54/xeX+vlNrjhT/tHf/ZUVxJr6aZzlRKJZRSH1NKfQDYBfwLeoThViAL/Bi4RURiJ/LwBsNyxgi8wVDZVAOuUiqrlPoc8FOl1Lh31Oor0fPcGS8fUHrr/yjwH8CDwPvRQ+dDXpbglLybp36Yt1AuJCIfBa4A/sq792dEJMgxUEr9HL2wr9gpyQCbgA8txtnZBkOlYQTeYKhsGoH0lOvi0PpqJofnV1M+XXcdcBNaZF1vu9sb0W/TAGERKXYIXiciTdM+M4qeBrhPKXUr+oz6tyml0szO48B69MLAM7173TmHcgaDYRpG4A2GyuZlwISI/LWIfBpYJyKXot/G70UPtzfjbYfz3rJ/opR6GP32nPH2zm9SSv3Qu+fXgSdF5D70HvVzpn6gUuoQegTgEhH5IfCcUup3c6zvDvRbfAHYiD7/vPVEHtxgWO6Y0+QMhgpGRK4HuoD70XvSBb3P/C3oue5fo8W92ytyQCnV45X9JNrYze+AZ5VS+Sn3XYvuABTn86d/bgPwWbRQbwUeA24HnlZKFY5R363oIfp3obfi5YFa9J76nulz+AaD4egYgTcYKhhvjnxCKfXCDGmnoufXt6NXr98DfFsplfHSTwMKRzGCc7TPOw+98r0B+KZSareIBICPANegBf+7wFeUUjunlLsMPdpQixb4NvSqfT96AWAAeFwp9Znj+wsYDMsXI/AGg2HJEREHPW8/ZN7SDYb5wQi8wWAwGAwViFlkZzAYDAZDBWIE3mAwGAyGCsQIvMFgMBgMFYgReIPBYDAYKhAj8AaDwWAwVCD/D3siZ3tw9o+IAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 卡方分布的概率密度函数图形\n",
    "\n",
    "# 生成模拟数据\n",
    "# 模拟数据\n",
    "x = np.arange(0., 14., 0.01)\n",
    "\n",
    "# 自由度（degree=1）的卡方分布随机数概率密度函数\n",
    "y = st.chi2.pdf(x, 1)\n",
    "\n",
    "# annotate 函数设置指向概率密度函数曲线的箭头和文字\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.annotate('degree=1', xy=(3, st.chi2.pdf(3, 1)),\n",
    "            xytext=(0.7, st.chi2.pdf(3, 1)-0.04), weight='bold', color='steelblue', fontsize=14,\n",
    "            arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='steelblue'))\n",
    "\n",
    "# 生成另一个模拟数据，下面几行代码同样功能\n",
    "y1 = st.chi2.pdf(x, 2)\n",
    "plt.annotate('degree=2', xy=(1.8, st.chi2.pdf(1.8, 2)),\n",
    "            xytext=(1.8, st.chi2.pdf(1.8, 2)+0.06), weight='bold', color='darkorange', fontsize=14,\n",
    "            arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='darkorange'))\n",
    "\n",
    "y2 = st.chi2.pdf(x, 4)\n",
    "plt.annotate('degree=4', xy=(3, st.chi2.pdf(3, 4)),\n",
    "            xytext=(3, st.chi2.pdf(3, 4)+0.06), weight='bold', color='g', fontsize=14,\n",
    "            arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='g'))\n",
    "\n",
    "y3 = st.chi2.pdf(x, 6)\n",
    "plt.annotate('degree=6', xy=(4.8, st.chi2.pdf(4.8, 6)),\n",
    "            xytext=(4.8, st.chi2.pdf(4.8, 6)+0.06), weight='bold', color='r', fontsize=14,\n",
    "            arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='r'))\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.plot(x, y1)\n",
    "plt.plot(x, y2)\n",
    "plt.plot(x, y3)\n",
    "\n",
    "plt.title('卡方分布概率密度函数', size=14)\n",
    "plt.xlabel('随机变量', size=14)\n",
    "plt.ylabel('卡方分布概率密度', size=14)\n",
    "plt.ylim(0., 0.4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a71abe07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 卡方分布的自由度极端高的曲线，这种情况极少见\n",
    "# 当自由度趋近于无穷时，卡方分布渐进服从正态分布，但是存在争议\n",
    "# 见：https://www.zhihu.com/question/363857851\n",
    "\n",
    "# 随机数\n",
    "x = np.arange(30., 90., 0.01)\n",
    "y5 = st.chi2.pdf(x, 60)\n",
    "plt.plot(x, y5)  # 曲线和正态分布钟形很相似\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62da2c69",
   "metadata": {},
   "source": [
    "#### 1.3.3 f分布的图形"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f117544e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# F分布不同自由度的概率密度函数的图形\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "\n",
    "# 生成模拟数据\n",
    "x = np.arange(0., 4., 0.01)  # 随机数\n",
    "# 自由度为3，20的F分布随机数概率密度函数\n",
    "y = st.f.pdf(x, 3, 20)\n",
    "\n",
    "# annotate函数设置指向概率密度函数曲线的箭头和文字\n",
    "plt.annotate('n=3, m=20', xy=(0.3, st.f.pdf(0.3, 3, 20)),\n",
    "            xytext=(0.3, st.f.pdf(0.3, 3, 20)+0.3), weight='bold', color='steelblue',\n",
    "            fontsize=14,\n",
    "            arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='steelblue'))\n",
    "\n",
    "# 生成另一个模拟数据，下面几行代码同样功能\n",
    "y1 = st.f.pdf(x, 7, 20)\n",
    "plt.annotate('n=7, m=20', xy=(0.6, st.f.pdf(0.6, 7, 20)),\n",
    "            xytext=(1.2, st.f.pdf(0.6, 7, 20)+0.2), weight='bold', color='darkorange',\n",
    "            fontsize=14,\n",
    "            arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='darkorange'))\n",
    "\n",
    "y2 = st.f.pdf(x, 20, 20)\n",
    "plt.annotate('n=20, m=20', xy=(1.5, st.f.pdf(1.5, 20, 20)),\n",
    "            xytext=(1.6, st.f.pdf(1.5, 20, 20)+0.2), weight='bold', color='g',\n",
    "            fontsize=14,\n",
    "            arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='g'))\n",
    "\n",
    "y3 = st.f.pdf(x, 20, 7)\n",
    "plt.annotate('n=20, m=7', xy=(2.25, st.f.pdf(2.25, 20, 7)),\n",
    "            xytext=(2.6, st.f.pdf(2.25, 20, 7)+0.2), weight='bold', color='r',\n",
    "            fontsize=14,\n",
    "            arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='r'))\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.plot(x, y1)\n",
    "plt.plot(x, y2)\n",
    "plt.plot(x, y3)\n",
    "\n",
    "plt.title('F分布概率密度函数', size=14)\n",
    "plt.xlabel('随机变量', size=14)\n",
    "plt.ylabel('F分布概率密度', size=14)\n",
    "plt.ylim(0.0, 1.1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "83ae1825",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# F分布的分位点填充图形\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 模拟数据\n",
    "x = np.arange(0.0, 4.0, 0.001)\n",
    "y = st.f.pdf(x, 5, 8)\n",
    "plt.figure(figsize=(8, 6))\n",
    "# label为 右上角显示图例\n",
    "plt.plot(x, y, label='alpha=0.1\\n n=5 \\n m=8')\n",
    "plt.title('F(5, 8)分布概率密度函数与分位点', size=14)\n",
    "plt.xlabel('随机变量', size=14)\n",
    "plt.ylabel('F分布概率密度', size=14)\n",
    "plt.ylim(0.0, 0.9)\n",
    "\n",
    "# 注意：scipy的ppf函数时，通过下分位来求分位数的\n",
    "# 置信度 = 1 - 显著性水平\n",
    "x1 = st.f.ppf(0.9, 5, 8)\n",
    "x2 = x[np.where(x>x1)]\n",
    "\n",
    "# axvline函数画垂直线\n",
    "plt.axvline(x=x1, ymax=st.f.pdf(x1, 5, 8)+0.01, ls='--', c='red')  # 添加垂直直线\n",
    "\n",
    "# fill_between 填充分布函数分位点的颜色，上0.1分位数对应的概率填充图\n",
    "plt.fill_between(x2, y[np.where(x>x1)], 0, facecolor='blue', alpha=0.3)\n",
    "plt.legend(fontsize=14)\n",
    "plt.show()\n",
    "\n",
    "# 左边空白部分为置信区间，右边为显著性水平"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9108b27b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
